SECURITIES AND EXCHANGE COMMISSION

                             Washington, D.C. 20549
                             ----------------------

                                    FORM 6-K

                        REPORT OF FOREIGN PRIVATE ISSUER

                    Pursuant to Rule 13a-16 or 15d-16 of the
                         Securities Exchange Act of 1934

                          For the month of April, 2004

                        Commission File Number: 000-21742

                               Stolt Offshore S.A.
                  ---------------------------------------------
                 (Translation of registrant's name into English)



                          c/o Stolt Offshore M.S. Ltd.
                                  Dolphin House
                                  Windmill Road
                                Sunbury-on-Thames
                          Middlesex, TW16 7HT, England
                          ----------------------------
                    (Address of principal executive offices)

     Indicate by check mark whether the registrant files or will file annual
reports under cover Form 20-F or Form 40-F.

                      Form 20-F   X             Form 40-F
                                 ---                      ---

     Indicate by check mark if the registrant is submitting the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(1): __

     Indicate by check mark if the registrant is submitting the Form 6-K in
paper as permitted by Regulation S-T Rule 101(b)(7): __

     Indicate by check mark whether by furnishing the information contained in
this Form, the registrant is also thereby furnishing the information to the
Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

                      Yes                       No   X
                            ---                     ---

     If "Yes" is marked, indicate below the file number assigned to the
registrant in connection with Rule 12g3-2(b): 82-________
<PAGE>
     In accordance with General Instruction B, attached herewith as Exhibit 99.1
is a press release issued by the registrant on April 23, 2004, announcing
financial results for the registrant's First Quarter (ended February 29, 2004)
of Fiscal Year 2004. The press release furnished pursuant to this Form 6-K shall
be deemed to be incorporated by reference into the registrant's Registration
Statement on Form F-3 (No. 333-86288) and to be a part of such registration
statement from the date of the filing thereof, to the extent not superseded by
documents or reports subsequently filed.

     Certain statements contained in the press release furnished pursuant to
this Form 6-K may include "forward-looking statements" within the meaning of
Section 27A of the Securities Act of 1933 and Section 21E of the Securities
Exchange Act of 1934. These statements may be identified by the use of words
like "anticipate," "believe," "estimate," "expect," "intend," "may," "plan,"
"project," "will," "should," "seek," and similar expressions. The
forward-looking statements reflect our current views and assumptions and are
subject to risks and uncertainties. The following factors, and others which are
discussed in our public filings and submissions with the U.S. Securities and
Exchange Commission, are among those that may cause actual and future results
and trends to differ materially from our forward-looking statements: the terms,
conditions and amount of our indebtedness; our ability to restructure our
indebtedness; our ability to recover costs on significant projects; the general
economic conditions and competition in the markets and businesses in which we
operate; our relationship with significant customers; the outcome of legal
proceedings; uncertainties inherent in operating internationally; the impact of
laws and regulations; and operating hazards, including spills and environmental
damage. Many of these factors are beyond our ability to control or predict.
Given these factors, you should not place undue reliance on the forward-looking
statements.
<PAGE>
                                    SIGNATURE

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.


                                            STOLT OFFSHORE S.A.


Date:    April 23, 2004                     By:       /s/ Alan B. Winsor
                                                --------------------------------
                                                Name:  Alan B. Winsor
                                                Title: Attorney-in-Fact