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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

jonesday.com

March 25, 2026

EDAP TMS S.A.

Parc d’Activités la Poudrette-Lamartine

4/6, rue du Dauphiné

69120 Vaulx-en-Velin, France

Re: Registration Statement on Form S-3 filed by EDAP TMS S.A.

Ladies and Gentlemen:

We are acting as special French counsel for EDAP TMS S.A., a French société anonyme (the “Company”), in connection with (A) the registration of the possible issuance and sale from time to time, on a delayed basis, by the Company of up to $125,000,000 in aggregate offering price of (i) ordinary shares, €0.13 nominal value per share, of the Company (the “Ordinary Shares”), (ii) preferred shares of the Company in one or more series, certain of which may be convertible into or exchangeable for Ordinary Shares (the “Preferred Shares”), (iii) warrants to purchase Ordinary Shares and/or Preferred Shares (the “Warrants”) or (iv) Ordinary Shares that may be issued up exercise of Warrants (the “Warrant Shares”), and (B) the registration of (i) warrants to purchase (a) up to 2,624,421 Ordinary Shares (the “Issued Selling Stockholder Warrants”) issued pursuant to the Warrant Agreement, dated October 17, 2025 (the “Warrant Agreement”), by and between the Company and the European Investment Bank and (b) up to 1,950,000 Ordinary Shares (the “Additional Selling Stockholder Warrants”) issuable pursuant to the Warrant Agreement and (ii) up to (a) 2,624,421 Ordinary Shares issuable upon exercise of the Issued Selling Stockholder Warrants (the “Selling Stockholder Warrant Shares”) and (b) 1,950,000 Ordinary Shares issuable upon exercise of the Additional Selling Stockholder Warrants (the “Additional Selling Stockholder Warrant Shares”), to be resold from time to time, on a delayed basis, by the selling stockholder (the “Selling Stockholder”) identified in the Registration Statement on Form S-3 as filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”) to which this opinion is filed as an exhibit (as the same may be amended from time to time, the “Registration Statement”), in each case as contemplated by the Registration Statement. The Ordinary Shares, the Preferred Shares, the Warrants, the Warrant Shares, the Issued Selling Stockholder Warrants, the Additional Selling Stockholder Warrants, the Selling Stockholder Warrant Shares and the Additional Selling Stockholder Warrant Shares are collectively referred to herein as the “Securities.” The Ordinary Shares, including the Warrant Shares issuable pursuant to the Warrants and the Selling Stockholder Warrant Shares and Additional Selling Stockholder Shares, as applicable, issuable pursuant to the Issued Selling Stockholder Warrants or Additional Selling Stockholder Warrants, as applicable, may be represented by American Depositary Shares. The Securities may be offered and sold from time to time pursuant to Rule 415 under the U.S. Securities Act of 1933 (the “Securities Act”).

BUREAUX: AMSTERDAM · ATLANTA · BOSTON · BRISBANE · BRUXELLES · CHICAGO · CLEVELAND · COLUMBUS · DALLAS

DETROIT · DUBAÏ · DÜSSELDORF · FRANCFORT · HONG KONG · HOUSTON · IRVINE · LONDRES · LOS ANGELES · MADRID

MELBOURNE · MEXICO CITY · MIAMI · MILAN · MINNEAPOLIS · MUNICH · NEW YORK · PARIS · PÉKIN · PERTH · PITTSBURGH

SAN DIEGO · SAN FRANCISCO · SÃO PAULO · SHANGHAÏ · SILICON VALLEY · SINGAPOUR · SYDNEY · TAÏPEI · TOKYO · WASHINGTON

March 25, 2026

Page 2

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:

1. The Ordinary Shares, when (a) the shareholders of the Company and, as the case may be, the Board of Directors of the Company (the “Board”), any holders of a specific category of securities of the Company and/or the chief executive officer (directeur général) of the Company, have taken all necessary corporate action to approve the issuance of, and establish the terms of, the offering of the Ordinary Shares and related matters, and (b) issued, sold and delivered in the manner and for the consideration stated in the applicable definitive purchase, underwriting, placement or similar agreement approved by the Board and/or the chief executive officer (directeur général) of the Company, as the case may be, upon payment of the consideration provided therein to the Company, will be validly issued, fully paid and non-assessable.

2. The Preferred Shares, when (a) the shareholders of the Company and, as the case may be, the Board, any holders of a specific category of securities of the Company and/or the chief executive officer (directeur général) of the Company, have taken all necessary corporate action to authorize and approve the issuance of, and establish the terms of, the offering of the Preferred Shares and related matters, and (b) issued, sold and delivered in the manner and for the consideration stated in the applicable definitive purchase, underwriting, placement or similar agreement approved by the Board and/or the chief executive officer (directeur général) of the Company, as the case may be, upon payment of the consideration provided therein to the Company, will be validly issued, fully paid and non-assessable.

3. The Warrants, when (a) the shareholders of the Company and, as the case may be, the Board, any holders of a specific category of securities of the Company and/or the chief executive officer (directeur général) of the Company, have taken all necessary corporate action to authorize and approve the issuance of, and establish the terms of, the offering of the Warrants and related matters, and (b) issued, sold and delivered in the manner and for the consideration stated in the applicable definitive purchase, underwriting, placement or similar agreement approved by the Board and/or the chief executive officer (directeur général) of the Company, as the case may be, upon payment of the consideration provided therein to the Company, will be validly issued.

4. The Warrants Shares, when (a) the shareholders of the Company and, as the case may be, the Board, any holders of a specific category of securities of the Company and/or the chief executive officer (directeur général) of the Company, have taken all necessary corporate action to authorize and approve the issuance of, and establish the terms of, the offering of the Warrant Shares and related matters and (b) issued upon exercise of the Warrants pursuant to the terms and conditions of the Warrants, will be validly issued, fully paid and non-assessable.

March 25, 2026

Page 3

5. The Issued Selling Stockholder Warrants have been validly issued.

6. The Additional Selling Stockholder Warrants, when (a) the shareholders of the Company and, as the case may be, the Board, any holders of a specific category of securities of the Company and/or the chief executive officer (directeur général) of the Company, have taken all necessary corporate action to authorize and approve the issuance of, and establish the terms of, the offering of the Additional Selling Stockholder Warrants and related matters and (b) issued, sold and delivered in the manner and for the consideration stated in the Warrant Agreement, upon payment of the consideration provided therein to the Company, will be validly issued.

7. The Selling Stockholder Warrants Shares, when issued upon exercise of the Selling Stockholder Warrants pursuant to the terms and conditions of the Issued Selling Stockholder Warrants and the Warrant Agreement, will be validly issued, fully paid and non-assessable.

8. The Additional Selling Stockholder Warrants Shares, when (a) the shareholders of the Company and, as the case may be, the Board, any holders of a specific category of securities of the Company and/or the chief executive officer (directeur général) of the Company, have taken all necessary corporate action to authorize and approve the issuance of, and establish the terms of, the offering of the Additional Selling Stockholder Warrant Shares and related matters and (b) issued upon exercise of the Additional Selling Stockholder Warrants pursuant to the terms and conditions of the Additional Selling Stockholder Warrants and the Warrant Agreement, will be validly issued, fully paid and non-assessable.

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 Ordinary Shares, Preferred Shares, Warrant Shares, Selling Stockholder Warrant Shares or Additional Selling Stockholder Warrant 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 Ordinary Shares, Preferred Shares, Warrant Shares, Selling Stockholder Warrant Shares or Additional Selling Stockholder Warrant Shares.

March 25, 2026

Page 4

In rendering the foregoing opinions, we have assumed that (i) the Registration Statement, and any amendments thereto, will have become effective under the Securities Act (and will remain effective at the time of issuance of any Securities thereunder); (ii) a prospectus supplement describing each class and/or series of Securities offered pursuant to the Registration Statement, to the extent required by applicable law and the relevant rules and regulations of the Commission, will be timely filed with the Commission; (iii) the resolutions authorizing the Company to issue, offer and sell the Ordinary Shares, the Preferred Shares, the Warrants, the Warrant Shares, the Additional Selling Stockholder Warrants and the Additional Selling Stockholder Warrant Shares and, if applicable, establishing the definitive terms of such Securities will be adopted by the shareholders of the Company at an extraordinary shareholders’ meeting, by the Board and, if applicable, by the chief executive officer (directeur général) of the Company, in accordance with the Company’s By-laws and applicable law, and will be in full force and effect at all times at which such Securities are issued, offered or sold by the Company; (iv) the Company will issue, and the Company and the Selling Stockholder, as applicable, will deliver the Securities in the manner contemplated in the Registration Statement; (v) the amount of Securities issued will remain within the limits of the then authorized but unissued amounts of such Securities; (vi) all Securities will be issued in compliance with applicable securities law; and (vii) the Warrant Agreement constitutes a valid and bind obligation of the European Investment Bank, and no provision of the Warrant Agreement has been varied or amended.

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. We are members of the Paris bar and this opinion is limited to the laws of the Republic of France. This opinion is subject to the sovereign power of the French courts to interpret 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 Registration Statement and to the reference to Jones Day under the caption “Legal Matters” in the prospectus constituting a part of such Registration Statement. 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 Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day