A couple of preliminaries:
Lascaux II is a reproduction for tourists. The original Lascaux has long been closed to all but reseachers. The very best caves for paintings (rivaling only Altimira in Spain) are at Pech Merle outside of Cabrerets.
The French national museum of prehistory in Les Eyzies is unique in the world.
The hike from the train/bus station out the causeway to MSM is a killer and will eat up your whole day. MSM is the most expensive spot in France, bar none including the riviera. Two hours will more than cover MSM. Make it a day stop and spend the night in maybe St Malo (the walled port complements the walled city at Carcassonne).
You can drive from Perigueux to St Malo/MSM in about six hours. Turning in the car, getting to a train, and riding it will cost you more in time and money than driving.
If the above makes sense, pick up the car in Brive and drop it in St Malo. If it doesn't make sense, put Carcassonne last on this part of your list and drop it in Toulouse which probably has pretty good train connections. I'm not a train guy, so take this with seventeen grains of salt.