Exhibit 5.1

PARTNERSHIP CONSTITUEE SELON LE DROIT DE L’OHIO, USA

AVOCATS AU BARREAU DE PARIS

2, RUE SAINT-FLORENTIN • 75001 PARIS

TELEPHONE: (0)1.56.59.39.39 • FACSIMILE: (0)1.56.59.39.38 • TOQUE J 001

WWW.JONESDAY.COM

August 14, 2026

EDAP TMS S.A.
Parc d’Activités la Poudrette-Lamartine
4/6, rue du Dauphiné
69120 Vaulx-en-Velin
France

Re: 8,425,000 ordinary shares in the form of American depositary shares issued by EDAP TMS

Ladies and Gentlemen:

We are acting as special French counsel for EDAP TMS, a French société anonyme (the “Company”), in connection with the issuance and sale by the Company of 8,425,000 ordinary shares, nominal value €0.13 per share (the “New Shares”), to be delivered in the form of an aggregate of 8,425,000 American depositary shares (the “ADSs”), each ADS representing one New Share, pursuant to the underwriting agreement, dated August 11, 2026 (the “Underwriting Agreement”), by and among the Company, TD Securities (USA) LLC and Mizuho Securities USA LLC, acting as the representatives of the several underwriters named therein.

In connection with the opinions expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of such opinions. Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that, as of the date hereof:

The term “non-assessable,” which has no recognized meaning in French law, for the purposes of this opinion means that no present or future holder of New Shares will be subject to personal liability, by reason of being such a holder, for additional payments or calls for further funds by the Company or any other person after the issuance of the New Shares.

In rendering the foregoing opinions, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals and the conformity to originals of all documents submitted to us as certified or reproduced copies. We have also assumed that (i) the resolutions authorizing the Company to issue, offer and sell the New Shares as adopted by the extraordinary shareholders’ meeting and/or the board of directors of the Company, as applicable, are accurately reflected in the minutes of such meetings provided to us, and remain in full force and effect and (ii) all New Shares will be issued in compliance with applicable securities and corporate law.

As to facts material to the opinions and assumptions expressed herein, we have relied upon written statements and representations of officers and other representatives of the Company and others. We are members of the Paris bar and this opinion is limited to the laws of the Republic of France as currently in effect. This opinion is subject to the sovereign power of the French courts to interpret agreements and assess the facts and circumstances of any adjudication. This opinion is given on the basis that it is to be governed by, and construed in accordance with, the laws of the Republic of France.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Current Report on Form 8-K filed on the date hereof by the Company and incorporated by reference into the registration statement on Form S-3 (File No. 333-294597) (the “Registration Statement”) filed by the Company to effect the registration of the New Shares under the Securities Act of 1933 (the “Securities Act”) and to the reference to Jones Day under the caption “Legal Matters” in the prospectus constituting a part of such Registration Statement and the final prospectus supplement, dated August 11, 2026 filed by the Company pursuant to Rule 424(b) under the Securities Act on August 12, 2026 relating to the New Shares. In giving such consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.