In 1990 we rented a car for a similar route. It was a lot of driving and I'm not looking forward to that; however, here was a great amount of convenience. Can this work with trains?
We took the fast train from Paris to Avignon (day trips to Nime, Pont du Gard & a minivan tour to lavender fields/Provence villages) and then to Carcassonne. Then we took a train to Toulouse to fly home. We both enjoy the leisure of taking the train to read books, walk a bit, and review our plans for the next location.
It isn't clear from your post whether you just want to get from Carcassonne to Paris, and look at the scenery along the way, or you want to stop and visit places of interest. Since you wrote "sites" instead of "sights," I'd assume it's the latter. For that purpose, I think a car would give you flexibility you'll appreciate, especially to visit places that don't have train service. You wouldn't need to drive it all the way to Paris, just to the last place you want to visit that has a rental office for whatever company you've chosen and also has train service to Paris. Could be Orly, or a city along your route.
The train will get you to or from Carcassonne faster than driving.
A car may be handy once you are there, or if you want to see places in between.
Flying home from Toulouse can really help extend what is possible for your itinerary.