Trains from Paris will arrive at Avignon TGV. There is a quick train (6 minute) that runs from Avignon TGV to Avignon Center usually twice an hour or so - check but usually 10 and 57 past the hour recently. There are multiple car rental agencies right outside the TGV station but little else including no left luggage/consignee facilities. You can buy a ticket for a couple of dollars for any train that day before you go or buy one there. If you buy one there cancel it on the station platform before you board but I was never checked for a ticket while riding the short train.
Avignon Center station is across the street from the city gates to Avignon and it is a quick and obvious walk. There are no left luggage facilities in Avignon Center but there is a place just inside the city that is mentioned on the train station website and other provate services like Luggage Nanny that fill this role.
https://pro.provenceguide.co.uk/533/new-la-consigne-luggage-lockers-in-avignon/
Your choices are essentially rent the car when you get into TGV, drive to Avignon and park it with your luggage in it. Or take the train to Center with your luggage, store it using one of the services, train back to TGV with your luggage, rent your car and leave from there. Both involve some hassle but depending on your travel style and the amount of luggage one of these options probably makes more sense to you.
The tourist office in Avignon has recently put together 3 different walking tours based on different interests that I thought were interesting.
People have reported that there is a car rental place in Avignon proper but also that it was booked up for all the times they tried. I rented from TGV so I don't know what the details are on renting in the city. This would save you a train trip back the TGV station but involve renting and driving in the city as opposed to the TGV station which is well outside the city proper.
Have a great trip,
=Tod
