Catania to France, and train or car in France?

My 21-yo daughter and I are planning a May-June trip to eastern Sicily and France, in part to revisit the places where she studied abroad (Siracusa and Montpellier; her real interest is Greek and Roman antiquities). I have found a reasonable fare from Dulles to Catania via Brussels, returning from Marseille, but am seeking advice on getting from Catania to France and on the first part of our trip in France. At this point we are tentatively planning to fly to Catania, spend a few days in Sicily, then fly EasyJet to Paris, spend a couple of days there, and head down south to Lyon, Montpellier, Nimes, Avignon etc. (I couldn't find a reasonable fare from Catania to southern France, and we'd be happy to have a few days in Paris.) We'd like to stop off in Lyon on the way. Once we get to the south, we'll probably want a car for at least part of the time. Does it make sense to rent the car in Paris at the end of our stay there and drive south? Or better to train from Paris to Lyon, stop off to visit a couple of museums, and get a car there? Or even continue by train to Nimes or Avignon and just rent the car for a day or two in the south? I am okay with driving if that makes the most sense (for example, we rented a car in the Loire valley so we could see the chateaux) but generally prefer to let someone else do it so I can look at the landscape. All comments and suggestions are most welcome, and Happy New Year to everyone on the Helpline!