Six weeks in France May-June

The French Riviera (NIce), the French Alps (Chamonix), Dordogne (La Roque-Gageac), Burgundy (Beaune), Alsace (Colmar) and Normandy (Bayeux) / Brittany (Dinan).

I'll throw the Loire valley in there. We were there in April and it checks all your boxes and it was Fabulous!

But will you stay in one spot and branch out from there? That's a lot of time in one place. I would do one week in six locations if I could go that long! At least two. (then I would pick Normandy, the Loire and Colmar/Strasbourg)

We spent 3 weeks September 2022 driving from Normandy to Nice. Our favourite spot was the Dordogne. We stayed in Sarlat and day trip to see cave art. The market was one of the best.
In Arles we drove to the nature reserve and saw flamingos which was amazing.

Amboise, Bordeaux, anywhere in the Dordogne, Avignon, Lyon, Colmar and back to Paris should be good bases.

Does anyone have experience with renting a gite? We are looking to do some relaxing and may not want to sightsee every day. Also, should we rent a car in Paris or take the train to different regions and rent once we get there? Our must list includes Normandy, the Loire valley, Burgundy and at least a little time back in Provence.

Your last post looks like you have 4 areas you want to explore more fully. I suggest splitting your 6 weeks into 4 stays of 10 nights each (approximately) which means finding a base in each area and branching out from there. Gives you time to day trip or relax and get to know your environs a bit better than even a week can provide. Interestingly,my husband and I have found that a minimum of 8 nights allows us to finally figure out the lay of the land in any location. By day 6 we are very comfortable with the surroundings and see so much more than when trying to figure out point A to point B!

I have rented through Gites de France several times, in 2017 and this year. It is my first place to look for accommodations in France, even if only for one night. This year in June, we had a great 4 bedroom, 3 bath house with a pool in the Dordogne, between La Roque Gageac and Vitrac for 10 nights. It sleeps 8; we were 7, and even though it was (for us) a deluxe place, it came out to $300.00 per night for 7 people! We would have needed three hotel rooms for all of us. What a bargain! FYI, it was through the Dordogne section of Gites de France and is called "Le Fort."

In 2017 we arranged 4 one-night stays through them and they were terrific bargains also, much better quality than nearby hotels and with lots more charm. Breakfast was always included and was superior to the buffet offerings in hotels. Homemade confitures and honey, croissants and bread, yogurts, fresh fruit and good coffee, are just some of what was available. Plus, meeting your hosts and having a personal interaction made our stays memorable. One offered dinner with our hosts and was a bargain at 25 euros each, considering it included, aperitifs, entrees, plats, cheese course and dessert. Wine and digestifs were included. we spent 3+ hours at the table in their home and felt like family.

FYI, here are the places we stayed, found through Gites de France, in 2017:

Villedieu les Poelles (near Mont St Michel) "Le Jardin de la Baissiniere",
Le Conquet (Far western point in Bretagne) "La Maison de Neuilly",
Chambord (where we had an evening "a table" with our hosts ") L'Oiseau de Paradis",
Pluneret (southeast part of Bretagne) "Les Chambres d'Hotes D'Evelyne".

I hope you are as fortunate as I have been with accommodations through Gites de France. (BTW, they are not paying me. I just find most of their choices to be ones I like.)

should we rent a car in Paris

I would not rent a car on arrival day.