Great idea in theory, but we quickly found that it could be expensive.
Bt we found a greta tip that could be of interest to some other forum members.
Origin Campervans rents small VW vans fully equiped, with very reasonable hire rates and unlimited mileage.
They are not in Paris but in Lille. We found that it was well worth the 50min train ride from Gare du Nord.
The vans are really well set up and have very cool designs !
The company name is Origin Campervans. They have a well detailed website.