The move highlights the extraterritorial reach of US policies and their potential impact on European corporate practices.
The companies have been told to confirm their compliance in a questionnaire entitled "Certification Regarding Compliance With Applicable Federal Anti-Discrimination Law".
US President Donald Trump's "America First" policies have stoked economic and political tensions between the US and Europe.
The US questionnaire raises questions about the practical changes targeted companies may need to implement, given the differing approaches between the US and France.
US companies have embraced Diversity, Equity, and Inclusion (DEI) policies, tracking race and ethnicity data and setting diversity targets.
In France, a secular approach limits such practices, with laws restricting data collection and corporate efforts focusing more on gender and socioeconomic background.
The questionnaire will also spark concerns in European boardrooms that the Trump administration is widening its fight against DEI policies overseas, at a time when Trump's actions on tariffs and security ties have upended transatlantic relations.
French business daily Les Echos, which first reported the US demand late on Friday, said it had been sent out to firms by the US embassy in Paris.
"We inform you that Executive Order 14173, Ending Illegal Discrimination and Restoring Merit-based Opportunities, signed by President Trump, applies to all suppliers and service providers of the US Government, regardless of their nationality and the country in which they operate," reads the letter, according to a copy that French newspaper Le Figaro published on its website.
"We would be grateful if you could complete and sign the document in English within five days and return it to us by email. If you do not agree to sign this document, we would appreciate if you could provide detailed reasons, which we will forward to our legal services," the letter added, with reference to the certification seen by Reuters.
An embassy spokesperson did not immediately respond to a request for comment.
'UNACCEPTABLE' There was no indication that the companies receiving the letter were selected based on their presence in the US, a source close to the matter confirmed that France's state-controlled telecoms group Orange, which has no US presence, received the letter.
Meanwhile, defence electronics firm Thales and oil major TotalEnergies, both with operations in the US, did not receive it, according to spokespeople for the companies. Orange declined to comment.
"American interference in the inclusion policies of French companies, along with threats of unjustified tariffs, is unacceptable," France's Ministry of Foreign Trade said in a statement sent to Reuters.
"France and Europe will defend their businesses, their consumers, and also their values," the ministry, which is under the authority of the country's Ministry of Foreign Affairs, added.
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