Exhibit 5.1

LOEB & LOEB LLP   345 Park Avenue   New York, NY 10154-1895 Main   212.407.4000 Fax    212.407.4990

February 13, 2025

CSLM Holdings, Inc.

2400 E. Commercial Boulevard

Suite 900

Fort Lauderdale, FL 33308

Re: CSLM Holdings, Inc.

Ladies and Gentlemen:

We have acted as United States securities counsel to CSLM Holdings, Inc., a Delaware Corporation (the “Company”) in connection with the Registration Statement on Form S-4 (File No. 333-283520) initially filed by the Company with the Securities and Exchange Commission (the “Commission”) on November 27, 2024 under the Securities Act of 1933, as amended (the “Act”). Such Registration Statement as amended, or supplemented, is hereinafter referred to as the “Registration Statement”. The Company has entered into a Merger Agreement, dated as of January 22, 2024, as amended on August 27, 2024 (the “Merger Agreement”) by and among the Company, CSLM Acquisition Corp., a Cayman Islands exempted company and the parent of the Company (“Parent”), CSLM Merger Sub, Inc., a Delaware corporation and wholly-owned subsidiary of Parent (“Merger Sub”), and Fusemachines Inc., a Delaware corporation (“Fusemachines”). Pursuant to the Merger Agreement, Merger Sub will merge with and into Fusemachines, with Fushemachines continuing as the surviving entity and as a wholly-owned subsidiary of the Company (the “Merger”). Prior to the effective time of the Merger (the “Effective Time”),the Company will merge with and into Parent with the Company continuing as the surviving entity in order to change from an exempted company in the Cayman Islands to a corporation incorporated under the laws of the State of Delaware (the “Domestication Merger”). The Domestication Merger is subject to the approval of the shareholders of the Parent

On the effective date of the Domestication Merger, among other things, (i) all of the currently issued and outstanding ordinary shares, par value $0.0001 per share, of Parent (the “Ordinary Shares”) will convert automatically by operation of law, on a one-for-one basis, into shares of Common Stock, par value $0.0001 per share, of the Company (the “Common Stock”), (ii) each of Parent’s currently issued and outstanding warrants (the “Warrants”), issued pursuant to that certain Warrant Agreement, dated January 12, 2022, by and between Parent and Continental Stock Transfer & Trust Company (the “Warrant Agreement”), will automatically become by operation of law (and pursuant to Section 4.5 of the Warrant Agreement) warrants to acquire Common Stock (the “Company Warrants”), and (iii) each outstanding unit of Parent consisting of one Class A Ordinary Share, one-half of one Warrant, and one right (collectively, the “Rights”) to receive one tenth of one Class A Ordinary Share issued pursuant to the Rights

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CSLM Holdings, Inc. Page 2

Agreement dated January 12, 2022 by and between Parent and Continental Stock Transfer & Trust Company (the “Rights Agreement”) will shall separate into each’s individual components of one Class A Ordinary Share, one-half of one Warrant and one Right, and all Parent Units shall cease to be outstanding and shall automatically be canceled and retired and shall cease to exist. .

This opinion is being rendered in connection with the registration under the above-referenced Registration Statement of up to (i) 28,541,535 shares of Common Stock (the “Shares”) (consisting of (a) 6,644,035 shares issuable upon conversion of the 6,644,0350,000 issued and outstanding Ordinary Shares into Common Stock (the “Conversion Shares”), (b) 1,897,500 shares of Common Stock issuable upon exchange of the Rights (the “Rights Shares”), (c) up to 20,000,000 shares of Common Stock issuable as consideration to the holders of the issued and outstanding shares of common stock of Fusemachines pursuant to the Merger Agreement (the “Merger Agreement Common Shares”), and (ii) 18,975,000 Company Warrants to purchase 9487,500 shares of Common Stock.

We have examined such documents and considered such legal matters as we have deemed necessary and relevant as the basis for the opinions set forth below. With respect to such examination, we have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to original documents of all documents submitted to us as reproduced or certified copies, and the authenticity of the originals of those latter documents. As to questions of fact material to this opinion, we have, to the extent deemed appropriate, relied upon representations of certain officers of the Company.

Based upon the foregoing, we are of the opinion that:

1. Upon the effectiveness and closing of the Domestication Merger, the Conversion Shares will be validly issued, fully paid and non-assessable.

2. Upon the effectiveness and closing of the Domestication Merger, each issued and outstanding Company Warrant will be a valid and binding agreement of the Company, enforceable against the Company in accordance with its terms.

3. Upon issuance in accordance with the Merger Agreement, the Merger Agreement Common Shares will be validly issued, fully paid and non-assessable.

4. Upon issuance in accordance with the Rights Agreement following the Business Combination (as defined in the Registration Statement), the Rights Shares will be validly issued, fully paid and non-assessable.

The opinions we express above are based upon a review only of those laws, statutes, rules, ordinances and regulations which, in our experience, a securities lawyer who is a member of the bar of the State of New York and practicing before the Commission exercising customary professional diligence would reasonably recognize as being applicable to the foregoing transactions. In addition, we have assumed that the effectiveness of the Reincorporation Merger will result in the Company assuming all rights, duties and obligations of Parent under the Warrant Agreement and the Rights Agreement by operation of the Companies Act (As Revised) of the Cayman Islands.

CSLM Holdings, Inc. Page 3

The opinion set forth in paragraph 2 above is subject to (i) the effect of any applicable bankruptcy, insolvency, reorganization, moratorium or similar law relating to or affecting creditors’ rights generally (including, without limitation, fraudulent conveyance laws) and (ii) the effect of general principles of equity, including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing and the possible unavailability of specific performance or injunctive relief, regardless whether considered in a proceeding in equity or at law.

We express no opinion as to the enforceability of (i) provisions that relate to choice of law, forum selection or submission to jurisdiction (including, without limitation, any express or implied waiver of any objection to venue in any court or of any objection that a court is an inconvenient forum) to the extent that the validity, binding effector enforceability of any such provision is to be determined by any court other than a state court of the State of New York or (ii) waivers by the Company of any statutory or constitutional rights or remedies. We draw your attention to the fact that, under certain circumstances, the enforceability of terms to the effect that provisions may not be waived or modified except in writing may be limited.

The opinions we express herein are limited to matters involving the internal laws of the State of New York and the applicable provisions of the DGCL. We express no opinion with respect to any other laws.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the reference made to us under the caption, “Legal Matters,” in the Registration Statement and in the prospectus constituting a part of the Registration Statement. In giving this consent, we do not hereby admit that we are in the category of persons whose consent is required under Section 7 of the Act, or the rules and regulations promulgated thereunder or Item 509 of Regulation S-K promulgated under the Act.

Very truly yours,

/s/ Loeb & Loeb LLP

Loeb & Loeb LLP