Rental car from Paris (vs train) to Lyon -Avignon

Do you want to make stops along the way from Paris to Avignon?

If no: Take the train
If yes: Are those stops between Paris and Lyon?

If yes: Rent a car in Paris
If no: Take the train to Lyon and rent the car there.

The Train is so quick and easy on the route from Paris to Avignon. Sit back and enjoy the Ride. Take day tours from Avignon. There used to be a circuit of Farmers Market around Avignon held on different days of the week that you could visit with a car. I might want to do a stopover at Lyons; especially if you are a foodie.

I would train to Lyon or fly to Marseille and rent the car there for touring Provence

I would train to Lyon or fly to Marseille

Why would you even consider flying from Paris to Marseille?

Train to Lyon or Avignon then get a rental car in one of those cities.

Specifically, there are two stations in Avignon and the station you want in your case is "Avignon TGV". This is where the high speed train stops and where car rental outlets are located.