Itinerary advice for 3 week trip in July

I wish you had more time in the Dordogne, but perhaps you can go there again if you anticipate additional trips to visit you friend in Pau? Pau also could link to time in the French Basque Country.

There are also a lot more worthwhile destinations in Brittany. I got around that part of France pretty well without a car, though I didn't go to Carnac.

Why not pick up car in Tours and drive to Sarlat?
Drop the car in Pau?

We returned a car to the Bordeaux airport, and it couldn’t have been easier. The signage for airports is usually good. The rental companies there are out on an open lot, so no multi-story edifices to navigate. What could be a problem?

As suggested above, I would also xonsider picking up the car in Tours (or nearby St Pierre des Corps) to drive to the Dordogne. It will be a 4:30 drive, to be compared to train + 2:15 drive, but you could see things on the way, including Oradour sur Glane if you can bear it emotionally.
I would then definitely keep the car to drive from Dordogne to Pau. You will save a lot of time and some backtracking. The driving is very easy, you quickly reach the A20 motorway from Sarlat, down to Toulouse, then onwards to Pau via the usually quiet A64.
In Pau, I do not know which car rental offices are at the train station vs at the airport. If there are more car rental offices at the airport, you could consider a flight to Paris (Orly).

Christine and Balso, thanks for the suggestion to drive to Pau and for the info about which motorways to take. I checked with Auto Europe and it looks like they don't have a drop off in Pau. Very surprising since as acraven points out how Pau can be a link to the French Basque country. Given our inexperience with driving in France, we'll start with a car in Bordeaux and look into doing a loop and return the car to Bordeaux after our stay in Pau. Roslyn, we'd be taking the car back to the Bordeaux train station rather than the airport. Thanks again everyone.

I checked with Auto Europe and it looks like they don't have a drop
off in Pau.

You might want to double check.
i just checked AutoEurope.com for random days in July- (weekdays and be sure to put in am times as most places close for the afternoon- then reopen 3:30-4) and see Europcar offered pick up in Tours and drop off at the Pau downtown location or the airport.

Just seems like a lot of extra travel to Bordeaux just to get a car.

We drove from Amboise to Sarlat without issues- stopped in Oradour sur Glane which was difficult but very worthwhile.

Thanks for checking, Christine. This time instead of indicating Gare de Tours, I hit 'all locations' and then was able to pull up Pau for the drop-off but only at the airport. We had originally wanted to stay in Amboise but chose to stay in Tours since it would give us easy access to the train. If we decide to drive, I'd like to pick up the car in Tours and drive to Amboise and stay there instead as I prefer to stay in a smaller town. Would you mind sharing the auto route that took to Sarlat from Amboise? Did you take the A20? We would definitely be interested in stopping by Oradour sur Glane as my husband is a history buff. Thanks again.

Here’s another endorsement for Oradour sur Glane. I got there this past October after trying to get there for years. It’s shocking to see. To wander those frozen-in-time streets and tour the museum - absolutely worth the drive out there to bear witness and pay respect.

Thanks, Valerie. You're the 3rd person to comment on the moving experience of bearing witness and paying respect at Oradour sur Glane. Here's the link that acraven posted recently: Oradour-sur-Glane.

Here it is again, history and humanity: https://en.wikipedia.org/wiki/Oradour-sur-Glane