tl;dr: In theory no, in practice yes.
Most national monuments (e.g. Louvre, Musee d’Orsay, …) are managed by the same organization and likely they stick to the same rules. I assume this is similarlay valid for other sights (e.g. Eiffel tower).
In theory:
The Louvre page on admissions states that entrance is free for
- disabled visitors and their guest or helper
and
A list of all acceptable proofs of entitlement is available at the museum from the Information Desk (under the Pyramid).
Now that is not very accessible and a French group for open access to culture has published this list. The page is in French so if you don’t read that it basically says you need a card from MDPH or CDAPH which seem French institutions to me (and a degree of the handicap of 80% or more).
Following the letter of this regulation, holders of foreign handicapped cards should not be granted the reduction. However I doubt this is the way it is handled in practice.
In practice:
A German issued card was accepted without hesitation for the card holder and an accompanying person (even when not specified on the card, regardless of degree of disability) at Musee d’Orsay. I assume similar policies are in place also for the other national monuments.
The formal document to be recognized as a disabled person in France can be obtained here : https://www.service-public.fr/particuliers/vosdroits/F2446
Obviously, this is not a realistic option for a traveler.
Nevertheless, someone sitting in a wheelchair will be considered as a disabled person, and no one will try to check whether he/she is really disabled (in most cases). I doubt that if you buy a disabled person ticket in advance and present with someone in a wheelchair any one will dare to ask for a proof, especially if you are foreigners. It might be less obvious with other kind of disabilities.
Notice that in the example you gave, and in most (if not all) places where there’s a free (or reduced fee) entrance for disabled person, the free (or reduced) fee applies to the disabled person and one accompanying person, not to a group of several persons. That is common in France.
Source : personal experience in France where I live and have a disabled relative.
Credit:stackoverflow.com‘