Logistics of returning rental car to Avignon TGV station

Your problem is that there's no luggage storage facility at the Avignon TGV station, which is on the south edge of town. So if you return the car first, what will you do with your bags? I think you're going to have to drive into town. Just head for the Palais des Papes. There is a large underground parking garage there. There is plenty to see on foot in that area after you park; you'll easily fill your time. By the way, there are two train stations in Avignon: Avignon Centre and Avignon TGV. Don't get confused between the two; I have seen it happen.

The LOCAL train station is at the south end of the tourist zone of Avignon, so it is within walking distance of everything. At the street intersection between the station and the town is where you can catch the shuttle bus (just a euro or two if I recall), which takes you between the Local and the TVG train stations. I don't recall if they have a baggage check at the local station, but I think they do. If they do, then I would return the car at the TVG station, take the shuttle to the local station, check the bags, and then walk around the town. When ready to go, just reverse this sequence. If you discover that there is no baggage checking at the station, then it is probably easier to leave your bags hidden in the trunk of the car and park the car in a parking lot (bring change in case that is how you pay to park at that one).
You can probably e-mail the car rental place in Avignon to ask them if there is baggage checking at the other train station there. Good luck.

Good work, Bruce. My only addition would be (assuming you are picking up the car at the TGV station) to ask when you pick up the car if they would be so kind as to allow you to leave your bags there for a couple of hours prior to the train departure.

thanks for the great suggestions. Glad to know about the bus, I would rather not drive into Avignon.