Provence

I guess it depends how much driving you want to do, or how far off the train tracks you want to go. We only rented a car for the wine road and took the train everywhere else.

It depends on if you want to spend time in/near Nice... car rental pick-ups are very easy both at Nice airport and at the TGV station in Avignon. I would not advise on having a car in Nice or along the Riviera. So if this is where you will stay, and are planning to head straight to Provence, then pick up in Avignon's TGV station. But if you want to stay around Mougins as a base, then yes, pick up the car at NCE. Likewise if you would want to spend any time in between NCE and Provence, like on the Cote d'Azur or visiting villages like Bormes-les-Mimosas... Forgot to mention that it would also be very easy to pick up at Avignon TGV and drop-off at NCE airport, or vice-versa, if you only would like to drive one-way...

I did this a couple of years ago...rented auto in Marseille, drove into the area of Avignon (Vaison la Roamaine) and then drove the car into Nice and left it at the office adjacent to the train station. Warning: Driving in Nice can be hazardous to your health!! But, if you are just going to the train station and turn it in you will be fine. I agree with the other posts re Riveria, etc.
Once you get the car in Nice and leave the city you will enjoy all.... To Beaune, I took the train after leaving the car in Nice.

I don't know if you have made your decisions yet but I would rent the car in Nice and drive to Arles, etc. The train would be faster but we enjoy seeing the roads rather than swishing by on the train. We even try to take some of the really small roads. The A autoroute is an easy road on which to drive. It would be an interstate in the US. There is a D road that almost parallels the A. If you have time, you can take detours to Cannes, St. Tropez, Hyeres, and Marseilles. When you are in Arles, I would go to the Camargue. I really loved seeing that area. Seeing the bulls, flamingoes and white horses was fun. In addition, we went to Aigues Mortes and Stes Maries de la Mer. Even the salt factories were interesting to see. Near Avignon, I would include going west to the Pont du Gard and Nimes. I would also see Les Baux between Arles and Avignon. We have travelled less in the wine areas except for Chateauneuf de Pape. Have fun!

Jet lagged I would take the train, settle in, pick up the car the next day.

If you're pooped and don't want to see the stuff along the way, ride the train. If it's a summer trip, ride the train. Personally, I'd drive and dwadle for a couple of days along the way - - at least one way.

If you are settled on arriving at the airport in Nice, the easiest solution is to rent a car. Perhaps, designate one of the passengers to map reading or get a GPS. Nice can be a stressful place to drive. But once you're on the road, I would suggest to head to Arles or Avignon ASAP. Unless your are incredibly dedicated to the area around Nice, I would recommend to high tail it out of there and seek the best sights around - in Arles and Avignon. Especially the wine region. My region, further north, towards Vaison-la-Romaine has the best wineries, restaurants and scenery. Enjoy your trip, Diane