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).
The Louvre page on admissions states that entrance is free for
- disabled visitors and their guest or helper
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.
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.