No car rental open at Avignon?
 

Eurocar told me the car rental office was closed at Courtine Avignon on Saturdays and Sundays. I would have to pick up the car at Roche. Hard to believe that there are no car rental offices open at the TGV station on a Saturday! All of the Parisians drive down?! I would have to leave my family cooling their heels at Courtine, take a taxi to the car rental that is open in Roche, then go back to Courtine. Does the TGV from Gare de Lyon stop at Roche?

Well they're not all closed on Saturday. We picked a car up from National at the TGV station on a Saturday last September, and I saw activity at some of the other companies. It certainly wasn't busy, though.

Try Autoeurope.

We just rented a car at Avignon TGV through Europcar (via Autoeurope). They were definitely open on Saturday.

Turns out there was a new agent at Autoeurope who was wrong. TGV station Auto rentals are open on Saturdays.
Lesson is not to accept something that sounds strange, double check everything!

Isn't that the truth, Edfran. It took me about 10 calls to tour agent, Finnair, and American for American to finally admit that, yes, I existed on a certain flight.