Should I stay or should I skip

If I had spent that much time in Paris on previous trips, I'd focus this one on the other destinations. You might be able to get to Amboise on your arrival day if the timing is right and you have the energy. Take a train, then rent a car there or nearby, preferably the next day so you're not driving after an overnight flight. The Loire has enough to see for several nights and Amboise is a good base. I agree with the previous poster about Carcassonne, one night is plenty. Stay in the old city if you can to enjoy it after and before the midday crowds. I haven't been to your other destinations, but I'm sure you could use more time there as well. Maybe there's a reason for the last four nights in Paris, but again you might get more value by adding them to your other places. You could drop the car at CDG, or another city with direct train service to CDG, the day before your flight home.

Your title reminded me of Joe Strummer....

Note that it's "Sarlat-la-Canéda" and not "Sarlat-au-Canada".

In France you can simply say Sarlat and everyone will understand (and it's easier to pronounce)

A recognized gastronomic specialty is the "pommes de terres sarladaises"" (sarladaises potatoes) that many French pronounce badly when saying "salardaises".
But whatever the pronunciation, it's very good. It's just potatoes cooked in goose fat with garlic and parsley.

That being said, I would also tend to remove one night in Carcassonne.
You can possibly spend it in Toulouse, the pink city, which is on the road between Sarlat and Carcassonne.

Sarladaises potatoes go very well with duck confit.

have you made your airline reservations? If not, and if you decide to omit Paris as a few posters suggest, you could fly open-jaw (or multi-city): into Paris and home from Nice. This saves you time from backtracking. You could spend more time in Nice and use that time to take the train along the French Riviera and visit places like Villa Grecque Kerylos, Villa Ephrussi, Villefranche Sur Mer, Menton, etc along the coast. And visit the hill towns in the area, too.

If you have already made your airline reservations in and out of Paris, you could still add more days to Nice, and then perhaps spend 2 nights in Paris (instead of 4) at the end of the trip.

Hi Diane, I would skip Carcassonne and give those two nights to Nice. There’s so much to enjoy around Nice and easy train or bus gets you all along that area. Carcassonne was barely worth an overnight in our opinion. We stayed at a hotel inside the walls, so we explored all of it.

Also agree that you could head straight to Amboise and combine all of your Paris time at the end.

I haven’t been to Sarlat, so I can’t advise on number of nights there. We’ve stayed at all of the other locations, and those amounts seem good. Have a great time in France!

One night in Carcasonne is enough. We enjoyed staying inside the walled city.

Take a train from Paris CDG to Amboise that requires a transfer at Saint-Pierre-des-Corps (3h). Do not drive on the day of arrival if crossing the Atlantic. The best French onion soup I’ve ever had was at Restaurant Anne de Bretagne in Amboise.
I also highly recommend adding nights in Nice and exploring the French Riviera. I stayed for six nights and was not bored. I like the suggestion of flying into Paris and out of Nice.

I remember years ago showing my Rick Steves guide to the restaurant owner after dining, thinking he would be surprised and impressed, he just rolled his eyes and said Yes I know

It depends how you're travelling, although I'm guessing you're hiring a car. Any other way you'd be spending all of your travelling days actually sitting around waiting for trains. Don't plan on hiring a car on Amboise, it's too small a town for that.

MaryPat. I'm not surprised to hear that about Anne de Bretagne. Usually their service is so slow that anything they deign to bring to the table is the best food you've ever eaten. Even so, the crepes are ghastly.

I too suggest your going directly to Tours/St Pierre des Corps, rent a car, and drive the relatively short distance to Amboise. Normally, I would not suggest driving after an all night, transatlantic flight, but the distance to Amboise is short, you will not be on an autoroute, and if you need an automatic, you will be much more likely to find one in Tours/St Pierre des Corps. Before you take a train to Amboise, you might check how far the station is from your hotel, it's a long walk, and taxi service will need to be arranged in advance, adding unnecessary complexity.

Two nights in Carcassonne are too much. I personally would skip Carcassonne completely and visit Aigues Mortes instead, which is less theatrical, much more authentic, and might fit your itinerary better. However, I understand that Carcassonne is a checklist item for many. Rather than actually staying in Carcassonne, you might look into spending the night in Minerve, the village from which Minervois takes its name. It's a beautiful setting and not yet flooded with tourists. I don´t think there are any hotels there, but there are a number of chambres d´hôtes. A table d´hôte would be ideal.

Staying a night at the airport before an early morning departure is fine if you are not already in Paris, but I would not uproot myself from a Parisian hotel simply to be at the airport the morning I depart. Would it not be much easier to spend your last night in Paris, and take either the RER B or taxi to the airport the morning of your departure? Plus, the restaurants at CDG are horrible. Enjoy your last night in Paris.

We visited Carcassonne (the citadel), too, and we really really enjoyed it. We stayed overnight in a hotel that is about a 5-minute walk from the citadel. We had an excellent dinner with gorgeous views inside the citadel. I don't remember the name but the food was delicious, much better than you would expect for a "touristy" location.