Paris to Sarlat

You have to decide what way is best for you. I'd probably take the train to Angouleme and drive from there. But if I had time I might plan a road trip with an overnight stop someplace enroute from Paris.

I doubt flying works very well, unless you can get really cheap tickets to Toulouse or Bordeaux.

Depending upon what time your plane lands, you may be able to take a TGV from CDG rather than having to go into Paris to catch a TGV there. What time does your plane arrive?

When you walk out the door of T2 at CDG, the rental car pick-up spots are just across the road. You'll need a car when you get to the Dordogne. From CDG, it's about a five hour drive; you'll go like a bat out of hell on the freeway from the moment you clear the ring road south of the city and won't slow down until you hit Brive.

Using the train, will involve one more mode of transportation change and probably add a bit to the bottom line for the trip.

Drive, keep it simple.