Driving in the Dordogne

The area has winding roads, but it is more hilly than mountainous and driving there does not constitute "mountain driving" in my view (as a very occasional driver from the lowlands). Obey the 50 mph speed limit (unless otherwise posted) and you will be fine. To further alleviate your fears, it might be worth purchasing a map of the area (Michelin are the best ones) as Google maps/navigation devices do not give easy-to-read info on road width and quality.
In any case, this part of France is rather tricky to visit without a car, alas.
Opinions on the driving may vary, of course.

Like the previous poster, I didn't have any trouble driving the roads around Sarlat-le-Caneda or elsewhere in the Dordogne. It's hilly terrain with curves, all the roads I recall were two-lane, it was important not to go too fast, and they were well marked. I don't recall a lack of guardrails giving me any anxiety. I don't think you can avoid roads like these to see the places you listed, and I don't think there's a practical way to visit them on a reasonable timetable without driving. On the upside, it's mostly very scenic.

Acraven travels all over Europe on public transportation, taking her time, and she may have advice for avoiding driving in this area. But her trips are measured in months rather than weeks.

You should be fine. The driving is nothing like, for example, the Amalfi Coast or California Rte. 1. Your gps will be of great help, but only if you spell the destination names correctly; c.f. Sarlat and La Roque-Gageac.

They do not have mountains in this region, so no need for guardrails. We found it very easy and wonderful to drive here. The only problem was the locals who wanted to drive faster than the limit and thus came up close behind us! So, we would pull over for them. Its an absolutely gorgeous area. Be sure to include Rocamadour!

Driving wasn’t bad with Michelin maps but parking can be a challenge in the picturesque towns. It takes patience and perseverance.

We have spent a couple of weeks on different occasions driving in the Dordogne. It is rural narrow roads and lots of traffic bottlenecks and so you don't get from one place to another speedily. I don't recall any scary mountain driving at all -- this area is rolling hills at most. The frustrations are traffic especially in high season. We choose to base in small towns rather than Sarlat as getting in and out of a larger city adds to the hassle. On the other hand, Sarlat has lots of amenities that small towns don't. We like to visit the markets and cook; the last small town we stayed in only had a couple of places to eat and one tiny bakery -- fine with us, but not if you are spending a week and plan to eat out int he evenings.

The only problem was the locals who wanted to drive faster than the limit and thus came up close behind us!

That's happened to me all over France; it goes with the territory.
As far as the Dordogne is concerned, the biggest concern with a car is parking. We've driven into Sarlat a few times, and parking was not so easy. And that was off season. We spent a week in Beynac, but luckily our gite had a private parking space. Driving was never a problem, but because of the winding nature of the roads, it often took longer than expected (especially in the days before Google Maps and GPS). We'd look at the map, see that our destination was not far as the crow flies, but the drive would take a very long time.

Driving in the Dordogne was easy. It's been a few years and even then driving with a GPS was easy. We wound up on several one lane roads through farms and woods and it was always a beautiful adventure. Lot's of traffic in Sarlat in the afternoon. Staying in Sarlat would give you plenty to do in the evening without having to drive after dark which is what I avoid. If you go to bed early you could stay in a smaller town which might be more scenic and less expensive.

We didn't have any trouble visiting Sarlat and the Lascaux caves on our road trip in 2018. For us, French mountain driving wasn't any more difficult than California mountain driving. If someone comes up fast behind you, just pull off at the first safe opportunity (as you might in the U.S.). Rent an automatic if you can. It's one less thing to distract you.

The drivers in France were way better than those in SoCal.