UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

SCHEDULE 13G

Under the Securities Exchange Act of 1934

(Amendment No.1)*

Criteo S.A.
(Name of Issuer)

Ordinary Shares
(Title of Class of Securities)

226718104
(CUSIP Number)

December 31, 2020
(Date Of Event which Requires Filing of this Statement)

Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

[x] Rule 13d-1(b)

[ ] Rule 13d-1(c)

[ ] Rule 13d-1(d)

* The remainder of this cover page shall be filled out for a reporting person's initial filing on this form with respect to the subject class of securities, and for any subsequent amendment containing information which would alter the disclosures provided in a prior cover page.

The information required in the remainder of this cover page shall not be deemed to be "filed" for the purpose of Section 18 of the Securities Exchange Act of 1934 ("Act") or otherwise subject to the liabilities of that section of the Act but shall be subject to all other provisions of the Act (however, see the Notes).

Persons who respond to the collection of information contained in this form are not required to respond unless the form displays a currently valid OMB control number.

SEC 1745 (3-06)


CUSIP No.226718104                     13G                     Page 2 of 8 Pages
--------------------------------------------------------------------------------
   1.  NAME OF REPORTING PERSON:
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON:

       Morgan Stanley
       I.R.S. # 36-3145972
--------------------------------------------------------------------------------
   2.  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP:

       (a) [ ]

       (b) [ ]
--------------------------------------------------------------------------------
   3.  SEC USE ONLY:

--------------------------------------------------------------------------------
   4.  CITIZENSHIP OR PLACE OF ORGANIZATION:

       Delaware.
--------------------------------------------------------------------------------
   NUMBER OF      5.   SOLE VOTING POWER:
     SHARES            0
  BENEFICIALLY    --------------------------------------------------------------
    OWNED BY      6.   SHARED VOTING POWER:
      EACH             4,357,880
   REPORTING      --------------------------------------------------------------
     PERSON       7.   SOLE DISPOSITIVE POWER:
      WITH:            0
                  --------------------------------------------------------------
                  8.   SHARED DISPOSITIVE POWER:
                       4,373,706
--------------------------------------------------------------------------------
   9.  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON:
       4,373,706
--------------------------------------------------------------------------------
  10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES:
       [ ]
--------------------------------------------------------------------------------
  11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9):
       7.3%
--------------------------------------------------------------------------------
  12.  TYPE OF REPORTING PERSON:
       HC, CO
--------------------------------------------------------------------------------


CUSIP No.226718104                     13G                     Page 3 of 8 Pages
--------------------------------------------------------------------------------
   1.  NAME OF REPORTING PERSON:
       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON:

       Morgan Stanley & Co. International plc
       I.R.S. #
--------------------------------------------------------------------------------
   2.  CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP:

       (a) [ ]

       (b) [ ]
--------------------------------------------------------------------------------
   3.  SEC USE ONLY:

--------------------------------------------------------------------------------
   4.  CITIZENSHIP OR PLACE OF ORGANIZATION:

       United Kingdom.
--------------------------------------------------------------------------------
   NUMBER OF      5.   SOLE VOTING POWER:
     SHARES            0
  BENEFICIALLY    --------------------------------------------------------------
    OWNED BY      6.   SHARED VOTING POWER:
      EACH             4,285,930
   REPORTING      --------------------------------------------------------------
     PERSON       7.   SOLE DISPOSITIVE POWER:
      WITH:            0
                  --------------------------------------------------------------
                  8.   SHARED DISPOSITIVE POWER:
                       4,285,930
--------------------------------------------------------------------------------
   9.  AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON:
       4,285,930
--------------------------------------------------------------------------------
  10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES:
       [ ]
--------------------------------------------------------------------------------
  11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9):
       7.1%
--------------------------------------------------------------------------------
  12.  TYPE OF REPORTING PERSON:
       BD, CO
--------------------------------------------------------------------------------


CUSIP No.226718104                     13G                     Page 4 of 8 Pages
--------------------------------------------------------------------------------

Item 1.     (a)   Name of Issuer:

                  Criteo S.A.
                  --------------------------------------------------------------
            (b)   Address of Issuer's Principal Executive Offices:

                  32 RUE BLANCHE
                  PARIS 75009
                  FRANCE
                  --------------------------------------------------------------
Item 2.     (a)   Name of Person Filing:

                  (1) Morgan Stanley
                  (2) Morgan Stanley & Co. International plc
                  --------------------------------------------------------------
            (b)   Address of Principal Business Office, or if None, Residence:

                  (1) 1585 Broadway New York, NY 10036
                  (2) 25 Cabot Square Canary Wharf, London E14 4QA, England
                  --------------------------------------------------------------
            (c)   Citizenship:

                  (1) Delaware.
                  (2) United Kingdom.
                  --------------------------------------------------------------
            (d)   Title of Class of Securities:

                  Ordinary Shares
                  --------------------------------------------------------------
            (e)   CUSIP Number:

                  226718104
                  --------------------------------------------------------------

Item 3.     If this statement is filed pursuant to Sections 240.13d-1(b) or
            240.13d-2(b) or (c), check whether the person filing is a:

            (a) [ ]  Broker or dealer registered under Section 15 of the Act
                     (15 U.S.C. 78o).

            (b) [ ]  Bank as defined in Section 3(a)(6) of the Act
                     (15 U.S.C. 78c).

            (c) [ ]  Insurance company as defined in Section 3(a)(19) of the Act
                     (15 U.S.C. 78c).

            (d) [ ]  Investment company registered under Section 8 of the
                     Investment Company Act of 1940 (15 U.S.C. 80a-8).

            (e) [ ]  An investment adviser in accordance with Sections
                     240.13d-1(b)(1)(ii)(E);

            (f) [ ]  An employee benefit plan or endowment fund in accordance
                     with Section 240.13d-1(b)(1)(ii)(F);

            (g) [x]  A parent holding company or control person in accordance
                     with Section 240.13d-1(b)(1)(ii)(G);

            (h) [ ]  A savings association as defined in Section 3(b) of the
                     Federal Deposit Insurance Act (12 U.S.C. 1813);

            (i) [ ]  A church plan that is excluded from the definition of an
                     investment company under Section 3(c)(14) of the
                     Investment Company Act of 1940 (15 U.S.C. 80a-3);

            (j) [x]  A non-U.S. institution in accordance with section
                     240.13d-1(b)(1)(ii)(J);

            (k) [ ]  Group, in accordance with sections 240.13d-1(b)(1)(ii)(K).
                     If filing as a non-U.S. institution in accordance with
                     sections 240.13d-1(b)(1)(ii)(J), please specify the type
                     of institution:  Not Applicable


CUSIP No.226718104                     13G                     Page 5 of 8 Pages
--------------------------------------------------------------------------------

Item 4.    Ownership as of  December 31, 2020.*

           (a) Amount beneficially owned:
           See the response(s) to Item 9 on the attached cover page(s).

           (b) Percent of Class:
           See the response(s) to Item 11 on the attached cover page(s).

           (c) Number of shares as to which such person has:

              (i)   Sole power to vote or to direct the vote:
                    See the response(s) to Item 5 on the attached cover page(s).

              (ii)  Shared power to vote or to direct the vote:
                    See the response(s) to Item 6 on the attached cover page(s).

              (iii) Sole power to dispose or to direct the disposition of:
                    See the response(s) to Item 7 on the attached cover page(s).

              (iv)  Shared power to dispose or to direct the disposition of:
                    See the response(s) to Item 8 on the attached cover page(s).

Item 5.    Ownership of Five Percent or Less of a Class.

           Not Applicable

Item 6.    Ownership of More Than Five Percent on Behalf of Another Person.

           Not Applicable

Item 7.    Identification and Classification of the Subsidiary which Acquired
           the Security Being Reported on By the Parent Holding Company.

           See Exhibit 99.2

Item 8.    Identification and Classification of Members of the Group.

           Not Applicable

Item 9.    Notice of Dissolution of Group.

           Not Applicable

Item 10.   Certification.

           (1) By signing below I certify that, to the best of my knowledge and
           belief, the securities referred to above were acquired and are held
           in the ordinary course of business and were not acquired and are not
           held for the purpose of or with the effect of changing or influencing
           the control of the issuer of the securities and were not acquired and
           are not held in connection with or as a participant in any
           transaction having that purpose or effect.
           (2) By signing below I certify that, to the best of my knowledge and
           belief, the foreign regulatory scheme applicable to a broker or
           dealer registered under section 15 of the Act (15 U.S.C. 78o) is
           substantially comparable to the regulatory scheme applicable to the
           functionally equivalent U.S. institution(s). I also undertake to
           furnish to the Commission staff, upon request, information that would
           otherwise be disclosed in a Schedule 13D.

*  In Accordance with the Securities and Exchange Commission Release
No. 34-39538 (January 12, 1998) (the "Release"), this filing reflects the
securities beneficially owned, or that may be deemed to be beneficially owned,
by certain operating units (collectively, the "MS Reporting Units") of Morgan
Stanley and its subsidiaries and affiliates (collectively, "MS").  This filing
does not reflect securities, if any, beneficially owned by any operating units
of MS whose ownership of securities is disaggregated from that of the MS
Reporting Units in accordance with the Release.


CUSIP No.226718104                     13G                     Page 6 of 8 Pages
--------------------------------------------------------------------------------

                                  Signature


After reasonable inquiry and to the best of my knowledge and belief, I certify
that the information set forth in this statement is true, complete and correct.


Date:       February 10, 2021

Signature:  /s/ Christopher O'Hara
            --------------------------------------------------------------------

Name/Title: Christopher O'Hara/Authorized Signatory, Morgan Stanley
            --------------------------------------------------------------------
            MORGAN STANLEY


Date:       February 10, 2021

Signature:  /s/ David Lindsay
            --------------------------------------------------------------------

Name/Title: David Lindsay/Authorized Signatory,
            Morgan Stanley & Co. International plc
            --------------------------------------------------------------------
            Morgan Stanley & Co. International plc


EXHIBIT NO.                        EXHIBITS                                 PAGE
-----------                        ----------                               ----

   99.1                       Joint Filing Agreement                          7

   99.2                       Item 7 Information                              8

*  Attention. Intentional misstatements or omissions of fact constitute federal
criminal violations (see 18 U.S.C. 1001).


CUSIP No.226718104                     13G                     Page 7 of 8 Pages
--------------------------------------------------------------------------------

                       EXHIBIT NO. 99.1 TO SCHEDULE 13G
                            JOINT FILING AGREEMENT
              ---------------------------------------------------


                              February 10, 2021
              ---------------------------------------------------

              MORGAN STANLEY and Morgan Stanley & Co. International plc hereby

              agree that, unless differentiated, this Schedule 13G is filed on

              behalf of each of the parties.


           MORGAN STANLEY

           BY: /s/ Christopher O'Hara
           ---------------------------------------------------------------------
           Christopher O'Hara/Authorized Signatory, Morgan Stanley

           Morgan Stanley & Co. International plc

           BY: /s/ David Lindsay
           ---------------------------------------------------------------------
           David Lindsay/Authorized Signatory,
           Morgan Stanley & Co. International plc


*  Attention. Intentional misstatements or omissions of fact constitute federal
criminal violations (see 18 U.S.C. 1001).


CUSIP No.226718104                     13G                     Page 8 of 8 Pages
--------------------------------------------------------------------------------

                                 EXHIBIT NO. 99.2
                                ------------------

                                ITEM 7 INFORMATION


             The securities being reported on by Morgan Stanley as a parent

     holding company are owned, or may be deemed to be beneficially owned, by

     Morgan Stanley & Co. International plc, a wholly-owned subsidiary of Morgan

     Stanley.

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