Taking my family including my elderly mother in law. Is there a place we can rent a wheelchair for portions of the day?
Go to the nearest pharmacy and ask. They will either rent them themselves or direct you to nearby pharmacy which does.
The key words you need to keep in mind are fauteuil roulant location.
Fauteuil roulant = rolling armchair = wheel chair
Location = rental
Tossing the word "tourisme" in there would probably help as well if you do an Internet search.
The two main sources will be pharmacies, as noted above, as well as stores using the term matérial médical -- medical equipment.
I'm assuming you're going to Paris. The Paris Tourism Office has some information on purveyors of medical equipment for rent. If you don't read French, it looks as if you can change the language in the upper right (the French flag icon).
Update: my apologies. For some reason the link did not come through, even though it showed in preview. Here's the relevant English language page: https://en.parisinfo.com/practical-paris/visiting-paris-with-a-disability/info/guides/practical-information-for-disabled-visitors/equipment-hire-for-disabled-visitors/rental-of-medical-equipment-including-wheelchairs