Comments/Suggestions on this itinerary

I would take a day/night from Avignon and add it to Nice or Paris. There is a years worth of things to see and do in Paris, and your first day will be less than "productive" after your flight. And you will lose a good half-day seeing Giverny (worth every minute!)

Agree with above-didn’t care much for Avignon

Why not train from Nice to Lyon?
Flight might be short but you still have to get to/from airports and deal with all security

First, congratulations on planning a great trip! I have a few suggestions, but they simply reflect my personal preferences.

I assume you will fly transAtIantic overnight and arrive in Paris early in the morning. I would save all the overnights in Paris for the end of the trip. This eliminates one hotel check-in and also avoids arriving at your first hotel hours before check-in time. You will undoubtedly be tired, but if you travel just another two hours from Paris you'll arrive in Tours. I'd also take one night from Paris and add it to Tours. You are planning to visit a number of chateaux but you might also want to visit the castle at Chinon or the Frontvraud Abbey.

I'd spend all the Provence time in one hotel, so perhaps cancel the overnights in Avignon and add those nights to Arles. The choice of Arles vs Avignon is often discussed in this forum, but I think Arles is more interesting with a greater range of restaurants and sites to visit. The choice between Arles and Avignon also depends on what day trips you plan to make. You may need a private driver to reach a few destinations in Provence, but the trip between Arles or Avignon and Marseille is an easy train ride.

For many people Bordeaux is a jumping-off point for the Dordogne/Lot area. Three nights in Bordeaux (about 2-1/2 days) isn't really enough time to see much outside of Bordeaux. That's fine if your plan is to concentrate on that city and maybe a side trip to St.-Emilion.