BFR Bbva Banco Frances S.A.

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SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

Report of Foreign Issuer

Pursuant to Rule 13a-16 or 15d-16

of the Securities Exchange Act of 1934

For the month of June 2016

Commission File Number: 001-12568

BBVA French Bank S.A.

(Translation of registrant’s name into English)

Reconquista 199, 1006

Buenos Aires, Argentina

(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of 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):

Yes   ¨             No    x

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):

Yes   ¨             No    x

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): N/A

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BBVA Banco Francés S.A.

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June 7, 2016

Securities and Exchange Commission

RE: Central Bank of Argentina approves cash dividends.

In my capacity as Market Relations Authority, I inform you that yesterday the Central Bank of Argentina through Resolution N° 306, authorized BBVA Banco Francés S.A to distribute earnings for a total amount of AR$ 900,000,000, corresponding to fiscal year 2015.

As was established in the Annual Ordinary and Extraordinary Shareholders meeting held on April 26, 2016, the Board of Directors will determined the date of the cash payment.

Sincerely yours

BBVA BANCO FRANCES S.A.

Reconquista 199 (C1OO3ABC) - Casilla de Correo 3196 Correo Central (C1OOOZAA) - B UENOS A IRES , A RGENTINA

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