I'm sure there will be several connections, but I wondered if you can take the train from Nice to Sarlat? Our RS tour ends in Nice. Also, how long will it take to take the train back to Paris from Sarlat?
Dawnya, the best place to go for information about trains is, oddly enough for France, the German rail website. http://www.bahn.com/i/view/GBR/en/index.shtml Since trains are often not scheduled far in advance, you can get a sense of what the options will be by ing a day next week that corresponds to the day of the week (Sunday, Tuesday, etc.) you will be interested in traveling. With regard to Sarlat: The entire region is so badly served by rail, and Nice is so far from it, that I think you will find this idea daunting. Too bad because it is a really great place. Moreover, if you get to Sarlat without a car I think you will wish you had wheels, and regret going to all the trouble to get there without any way to get about. (Well, you can always hire a driver.) For this reason in your position I might take the train as far as Toulouse and drive the rest of the way, or else fly to Toulouse and Bordeaux and drive from the airport.
As Adam pointed out, it will be a lengthy trip and a car is nice in Dorgogne. Train time from Nice to Sarlat is a minimum of 13 hours with at least one transfer. Sarlat to Paris is around 7 hours with most itineraries either overnight or late night arrivals in Paris.
I agree that while Sarlat is beautiful, train service there and around it, is poor, especially from Nice. You might want to consider more easily-reached alternatives, such as Marseilles, Arles, or Lyon.