Paris/Normandy/Loire/Provence logistics

Hi!
Since you fly out of Paris, you need to stay in Paris the last night, so I suggest that you end your trip with the Paris nights. I suggest 5 nights rather than 4, unless you have been to Paris before - and accordingly, 6 nights in Provence will do, rather than 7.

Therefore, on arrival day, I would "press on" to your furthest destination and take the train from the airport to Provence. Yes, it will be a long day, especially with the kids, but that arrival day is basically "lost" to exhaustion and jet lag anyway.
You can head to Avignon TGV station, rent a car there, and head to a nearby town as a base. Saint-Remy-de-Provence is most people's top choice with a car, and it is only a 20-minute drive from Avignon TGV. Nearby villages like Eygalieres or Fontvieille are also good, as well as L'Isle-sur-la-Sorgue or Pernes-les-Fontaines a bit further east (more like 30-40 minutes from Avignon TGV).

After that, the most logical destination is probably the Loire, because there are some train connections from Avignon TGV to Tours (Saint Pierre des Corps) that do not involve the much-dreaded transfer between stations across Paris. If you play around with the schedules, you will find a few connections through either Lyon, Massy TGV or Marne La Vallée TGV. Just be mindful of car rental hours at destination. And yes, Amboise is a very good base.

Amboise to Normandy is a relatively short drive, Le Mans is an interesting mid-way stop. The classic base for Normandy is Bayeux, and for good reason: charming town right next to the D-Day beaches. This said, if you are more interested in the natural landscapes and older historical sights of Normandy rather than the beaches, it is better to stay further east: Honfleur, Pont Audemer, Etretat, villages near the Seine downstream from Rouen...
And depending on your choice you can return the car in Caen, Le Havre or Rouen and take the train back to Paris.

I don’t know how old your children are, but I think you are trying to cover too much ground. Your first day or two in Paris is likely to be lost to jet lag. If you haven’t been to Paris before, you are short changing it and there is more to do here for children.

Unless Provence is a must, I would drop it and have a week in Paris and a week split between Normandy and the Loire. This means you don’t lose 2 days travelling to and from the south unless you can fly open jaw.

Paris - Bayeux - Amboise makes sense. I prefer staying in smaller places, but with children, it makes more sense to head for somewhere larger.

https://community.ricksteves.com/travel-forum/france/normandy-brittany-thoughts

Thanks everyone for the input. Kids are 16 and 13 and we have been to Paris before. Really would like to make Provence happen!

We went to Provence pre-kids, and did a lot of outdoorsy stuff as it was spring and we had lovely weather. Loved going to Pont du Gard, driving through the Gorge de la Nesque, driving up Mont Ventoux, and visiting Cassis and the calanques. We stayed in an apartment in Pernes les Fontaines and it was pretty convenient.

Could you fly into Paris and out of Provence or the reverse to make your criss-crossing easier, since you want to prioritize Provence? Agree with others that having 2 stays of only 3 nights is going to be a lot of traveling and not a lot of time to see stuff in those places.

Have to fly in and out of Paris. And am now thinking axing Loire and just focusing on Paris Normandy and Provence. We’ve been to Paris so maybe:
4 nights Paris
4-5 nights Normandy
5-7 nights Provence
Other thoughts on best way to travel amongst locations?