So here's my suggestion; September is a beautiful time and I'm also looking at honeymooning the same time in a Paris, Burgundy, Alsace, Champagne, Paris loop.
Hiking: No better place than Chamonix area.
Small Villages: No better place than Burgundy and Alsace. Alsace villages are half-timbered (think of the village in Beauty and the Beast). Each town is prettier than the last. Burgundy has medieval stone villages, also each town is prettier than the last. Use the cities for bases but don't neglect to see the villages.
I don't agree that every restaurant is good in France. After visiting Beaune my rule of thumb became, if it doesn't require reservations, you probably don't want to eat there. I don't usually reserve and had some horrible meals in Beaune (I wished I'd gone to a grocery store and bought a pre-made sandwich). Ask your lodging to help you book dinner reservations. They know the good places and will bridge the language gap reserving a table for you.
Start with staying in Antibes instead of Nice. Antibes has the nicest beaches, a nice Marina, wall, ramparts, a medieval center and a small restaurant/cafe area (plus one of the top art galleries) all in a walkable package. You can always catch the local train into Nice (there are three Nice stops, the first about fifteen minutes from Antibes, the other two are ten or fifteen minutes apart). Use the train, not a car, for getting around the Riviera.
As far as linking it together, I'm not sure I have the best advice. I visited as parts of three separate trips.
I'm a fan of Michelin Green Guide. They have some coverage of every little town. The books aren't large because they're broken down into smaller regions - but they're heavy. My only gripe is I wish they had an ebook option (I like to travel light). For lodging, I like to use TripAdvisor and Airbnb and rarely book in advance. I avoid Booking.com and Hotels.com because my worst experiences have been through them.