I can't tell you where you should pick up the car, since multiple factors are involved, but you will need to check railway schedules (are you coming from Paris?) to find the best combination of travel times and convenience. Your great good fortune is that there are many knowledgeable people on here, some of whom are resident in the area who can give you good advice.

What I can add is a few notes on provincial France. Most towns and many smaller cities have very different business hours than Anglo-Saxons are used to. It would not be uncommon to find businesses, including car rentals, closed for a long lunch (1 to 3 or even 4) and closed Saturday afternoons and perhaps all day Sunday, so you need to ensure that the place you want to rent is actually open when you want it to be. It is a good idea anywhere to take detailed photos of the car when you pick it up and when you return it, especially if you are having to use an after hours key drop.

The good news is that it is a fairly easy area to drive in. Roads are well marked, and there is usually parking outside the smallest towns and near the edge of things in larger towns like Sarlat itself. It is also very, very beautiful.

Great tips thanks Ackislander - things I wouldn't necessarily have thought of. Yes we are coming from Paris.

First of all, you cant get the train 'all the way to Sarlat' You would have to get off at Souillac and then take the coach (that normally meets the train) into Sarlat. Once you are there the only car hire agency is Europcar. If you want to spend some time in Sarlat itself before exploring the region, this is a reasonable option. HOever, I just re-read your note, and I see that you are heading for Beynac.

In that case, probably the easiest is to get the train to Brive and pick up a car there - most agencies have offices there, and the drive is quite easy. It takes about 45 minutes to an hour to get to Beynac. Still easier than getting a coach to Sarlat, finding Europcar, getting the car and heading out to Beynac.

Another option is to fly to Brive. Have alook at the airport site to compare costs and timing. YOu can pick up a car there.http://www.aeroport-brive-vallee-dordogne.com/en

the other side of the road--right or left?

Brive is probably the simplest and most straightforward, but coming from Paris you do have several options:

CDG or Gare Montparnasse TGV to Bordeaux, where there are loads of car rental options - then you have about a 2.5-hour drive to Beynac.

CDG or Gare Montparnasse to Libourne, where you have a few rental car options - then a 2.5-hour drive to Beynac.

Gare d'Aussterlitz to Périgueux (through Limoges, sometimes with just a 10-minute stop, sometimes with a brief change of train) - a few rental car otpions in Périgueux, and then you have about a 3-minute drive to Beynac.

StCirq-is the Libourne train a TGV, or not?

Yes. I suppose it's possible there are non-TGV trains to/from Libourne, but every one I've ever been on was a TGV.

Oops, just noticed a typo above - that's 30-minute drive to Beynac, not 3-minute.

Thank you all
I will look into our options from Brive and Perigeuex bearing in mind train times, flight options and rental car opening hours.
I now know what Intercites Autocar means on the train schedule - thank you Carlux. I figured it must be a coach.
That 3 minute drive sounded appealing for a moment StCirq!

'I now know what Intercites Autocar means on the train schedule - thank you Carlux. I figured it must be a coach.'

I have over the years had people swear to me that there is a train from Souillac to Sarlat, because they have booked it. Since they would have to challenge all the cyclists on the path where the tracks used to be, this is unlikely. But people dont always pay attention. Similar to people who assure me that they can drive up a pedestrain street in Sarlat because their GPS says 'turn right at...'