Itinerary Advice for 2 week French Trip

Just a couple suggestions: In the Loire Valley, in addition to Chenonceau, consider Château de Cheverny and Château de Chambord. In Amboise I loved the Château du Clos Lucé - not a proper huge château like the others, but a lovely small estate with garden where Leonardo da Vinci spent his last years. I loved standing right in his bedroom, no doubt in the very place he stood looking out the leaded glass window onto his small Renaissance garden. Also, there are full-size models of several of his inventions in the bigger garden. For Roman 'ruins' in Provence: the Pont du Gard, the Théâtre antique d'Orange in Orange (north of Avignon), and the Amphitheater in Arles (Arènes d'Arles). There's so much...

Just my opinion but. This is not a good use of time. You have packed too much into your 2 weeks and are spending much too much of it on the road. You say you really want Roman ruins and Provincial countryside, but you spend only 3 days there. The three best places on your itinerary are Dordogne, Provence, and Paris. If you are very nimble you can spend 3 days in each. More would be better. Fly into Toulouse or Bordeaux. Drive to Beynac etc. Spend enough time there to make it worth the trouble and expense. Drive to Provence. See some highlights. Train to Paris, fly home. Or reverse.

I agree that it's a LOT of driving for a two week trip. It's about 300 miles from Amboise to Avignon. Instead, why not rent the car the Amboise, tour the chateaus and then drop it off, hop the train to Nimes and then pick up a car there? This will free up significant time! While in the south of France, you might enjoy a visit to Avignon - home of the french papal palace.
Driving in France is not difficult at all.

It's a lot to cover in two weeks, imho. I haven't been to Provence or Riviera but you don't seem to have much time there for all your interests. Just one full day in the Dordogne will let you see perhaps one cave and one castle. The Loire chateau advice above is all good (plus don't forget the chateau at Amboise overlooking the river, separate from Clos Luce which is also very good). You can probably visit all those sites in the time you have since they're close together. I think Amboise and Beynac are good base town choices, easy to get in and out of with good things to see right there. Driving in France isn't hard, especially in the countryside. The autoroutes are an LA driver's fantasy of what a freeway should be, except not free, not at all. The country roads are narrower than we're used to but the cars are smaller. Check the RS France guide, or another good one like Lonely Planet, for the subtle differences in right of way, road signs etc.

Appreciate the prompt responses! I agree it's a lot of travel time; however, unless I'm missing something, even taking the train from Amboise to Nimes is going to require 6-7 hours, since everything connects back through Paris. I figured if we're going to haul all that way down to Provence, we'd use the short stint in the Dordodgne to break up the big travel stretches. Is there a faster option between the Loire and Provence I'm missing? Or... If we cut out the Dordogne entirely, and essentially started in the Loire.
Our flight arrives in Paris at 830am on Saturday, so we could conceivably get right on the train to Amboise. Spend a few days seeing castles, bounce back to Paris in the middle of the trip for a few days, and then train down from Paris to Provence. That assumes our flight arrives on time, etc.

You could go by train or if you drive there is an autoroute going down the center of France that you'd take from Amboise to Nimes. You don't have to go further west to the Dordogne to go south.

I think plan no 2 works well enough, and without a car a one-day stop in the Dordogne makes zero sense. I like starting in Amboise, but if that is untenable sacrificing one day for the long trip to Provence seems perfectly reasonable to connect these dots. You really are going to miss a lot of what you say you want to see in Provence without a car. It's not that you can't get to places so much as that you can't get to places easily enough to see much in a few days. I assume you have a plan to get about in the Loire without wheels (a tour?) or I would say the same thing there.