Exhibit 5.1

FOLEY & LARDNER LLP ATTORNEYS AT LAW   321 NORTH CLARK STREET, SUITE 3000 CHICAGO, IL 60654-4762 312.832.4500 TEL 312.832.4700 FAX WWW.FOLEY.COM   CLIENT/MATTER NUMBER 118491-0101

August 2, 2021

Invesco Specialized Products, LLC

3500 Lacey Road

Suite 700

Downers Grove, IL 60515

Re: Invesco CurrencyShares^® Euro Trust

Ladies and Gentlemen:

We have acted as legal counsel to Invesco Specialized Products, LLC, a Delaware limited liability company (the “Company”), in connection with the preparation and filing under the Securities Act of 1933, as amended (the “Act”), and the rules and regulations of the Securities and Exchange Commission (the “SEC”) promulgated thereunder, of a registration statement on Form S-3 filed on or about the date hereof (the “Registration Statement”). The Registration Statement relates to the proposed issuance by the Invesco CurrencyShares^® Euro Trust (the “Trust”), an investment trust formed on December 5, 2005 under the laws of the State of New York pursuant to the terms of the Depositary Trust Agreement dated December 2, 2005 and amended as of November 13, 2008, March 6, 2012, April 8, 2013, September 5, 2017, June 4, 2018 and January 9, 2019 (as so amended, the “Trust Agreement”) between the Company, as sponsor, and The Bank of New York Mellon, a banking corporation organized under the laws of the State of New York (f/k/a The Bank of New York), as trustee (the “Trustee”), of an indeterminable number of shares, representing units of fractional undivided beneficial interest in and ownership of the Trust (the “Shares”). In connection with the issuance of Shares, you have requested our opinion with respect to certain legal matters. Capitalized terms not otherwise defined herein shall have the meanings given to them in the Trust Agreement.

In rendering the opinion expressed below, we have examined and relied on the Registration Statement and originals or copies, certified or otherwise identified to our satisfaction, of the Trust Agreement and all such other documents as we have deemed necessary or appropriate in order to enable us to render the opinion expressed below.

In our examination of the foregoing documents, we have made the following factual assumptions, with your consent: that all documents reviewed by us are original documents, or true and accurate copies of original documents, and have not subsequently been amended; that the signatures on each original document are genuine; that all factual representations and statements set forth in such documents are true and correct; and that all obligations imposed by any such documents on the parties thereto have been or will be performed or satisfied in accordance with their terms.

In rendering the opinion stated below, we have relied with respect to certain factual matters solely upon the representations, certifications and other information contained in the documents referred to above and upon certificates of public officials. We have not made or undertaken to make any independent investigation to establish or verify the accuracy or completeness of such factual representations, certifications and other information.

The opinion stated below is limited to the laws of the State of New York and the federal laws of the United States of America, and we express no opinion in this letter as to the laws of any other jurisdiction. We express no opinion in this letter as to the application of the securities or “blue sky” laws of any state, including New York, to the issuance and sale of the Shares. This opinion letter is limited to the specific issues addressed herein; and no opinion may be inferred or implied beyond that expressly stated herein.

Our opinion is based solely upon the law and the facts as they exist on the date hereof; and we disclaim any obligation to advise you of any subsequent change in law or facts or circumstances that might subsequently come to our attention.

Based on the foregoing and subject to the limitations and qualifications set forth in this letter, we are of the opinion that the Shares, when issued and sold in accordance with the terms of the Trust Agreement (including the receipt by the Depository, on behalf of the Trustee, of the consideration required for the issuance of Shares), will be duly authorized, legally issued, fully paid and non-assessable.

We hereby consent to the filing of this opinion letter as an exhibit to the Registration Statement and to the use of our name where it appears in the Registration Statement. In giving this consent, we do not admit that we are within the category of persons whose consent is required by Section 7 of the Act or the rules and regulations of the SEC promulgated thereunder.

This opinion only relates to the issuance and sale of the Shares pursuant to the Registration Statement and may not be relied upon by you or any other person for any other purpose, without our prior written consent in each instance.

Very truly yours,

/s/ Foley & Lardner LLP