Don't know about Uber, but there are plenty of reliable cab drivers on the island. When he drops you off at the restaurant, he will give you a card. Restaurant will call him when you are ready for the ride back. Maybe someone else will know specifically about Uber.

You are wise to have someone else do the driving. The presumptive level on the island is low, perhaps .05 and the French police have no sense of humor. They often do road blocks to check for violators. Also, use the seat belt; they like to issue fines for those violations as well.