I wrote an email enquiry to the Louvre as a proxy to all regulated museums in Paris. It took longer than expected, but the result was worth the wait...
It is with great attention that I read your email.
I inform you that in compliance with a governmental regulation, the
Musée du Louvre is free for visitors under the age of 18 as well as
for the 18-25 year-old residents of the European Economic Area. A
valid ID or a proof of entitlement will be required at the entrance.
No ticket is required.
On Friday evenings from 6 p.m. to 9:45 p.m., admission to the
collections is free for under-26s regardless of nationality (upon
presentation of the ID or the passport, a driving licence or a
learner’s permit can be tolerated).
On the day of your visit, please join the line for visitors “with no
tickets” just in front of the main Pyramid. Please note that further
information on the Louvre admissions and fee policy is available on
our website: http://www.louvre.fr/en/hours-admission You will
find exhaustive information on specific conditions provided to young
visitors. I hope I have answered your questions and addressed your
concern. Please do not hesitate to contact us should you have any
further questions. Yours sincerely,
Name redacted, Service de l'accueil, Musée du Louvre
So the answer is yes, a UK driving permit (including a provisional permit) will easily suffice as a qualifying form of identification.
Museum policy in France is promulgated and regulated by the Ministry of Culture.