I'm a wee bit shocked by this. Surely that's something that you assume but still check when renting a car?

Citroën Bernard Frères Réparateur agréé
1440 av Amandier 84000 AVIGNON
Tel 04 90 89 91 94

Opening hours Mon-Fri 08h00 - 12h00 and 14h00 - 18h00. Not open Sat and Sun.

Hope this helps, but do enjoy Avignon and have a bit of down time. At least if you're not driving you can enjoy a glass or even more of the good local wine.