Feedback on our itinerary

Unless you plan lots of day trips/hikes/bike rides from Vaison-la-Romaine, a week is far too long there, IMO.
The Dordogne needs at least 5-7 days. A car is really necessary here, but biking options are a nice addition. Many of "Les Plus Beaux Villages de France" are here. Lots of small towns with markets, pretty drives (car or bike), prehistoric caves (do at least one!), castles from the Hundred Years War, and kayaking or canoeing on the beautiful Dordogne River. (we have river rafted on some great rivers here in California, but the Dordogne is truly special.) Also, the local food specialities are delicious.

One hint...drive times listed in Google or Viamichelin are underestimated. They make no allowance for gas/food/comfort stops. We almost always drive when in France, and I use Viamnichelin for drive times, routes, etc., but I always add 1-2 hours cushion, depending on the drive length. Of course, we mostly take the smaller D roads for the scenery, not the Autoroutes. Viamichelin usually gives 2 or 3 route options (fastest, most economical, most scenic, etc.)

I don't know the Gorges Du Tarn, Murat or Correze, so I have no recommendations for you.

Have fun!

I disagree that a week is too long in Vaison. Besides, Gite rentals are often weekly, so I guess you have to stay for 1 week?
There is a lot to see and do in the area, and you can easily travel as far as the Pont du Gard or the Luberon for sightseeing purposes.
Now, if you don't have to stay a full week, you could reduce to 6 days and add 1 day to your stay near Brive

However, 4 days / 4 nights in the Gorges du Tarn sounds like a long time. 3 days is probably enough to enjoy it.
Add 1 night to your stay near Brive instead, as you do need more time to see the Perigord and the Quercy.

3 nights in Murat is good. I do not know Murat itself, but the Monts du Cantal are stunning, with fantastic hiking. Make sure to visit Salers, too.

As for the town east of Lyon: which one do you have in mind?

General comment: driving around the gorges du Tarn is on very twisty, narrow roads. Cantal and Corrèze also have many such roads, but some main roads are actually pretty fast - it depends. Don't try to keep pace with locals, though!

Here's a map that might help you with your trip to the Gorges du Tarn.

https://www.google.com/maps/d/edit?mid=1SrAtdgxHVZnob6W3FwLoW4bqrLmZCuU&usp=sharing

Since you estimated a 4-hour drive from Vaison-la-Romaine, I've added a layer with a route to Ambialet that roughly corresponds to that driving time. I don't know if this is the route you want to take, nor where the hotel you found is located.

I would tend to agree with Balso about shortening your stay in the Gorges du Tarn to 3 nights instead of 4. But it all depends on what you find to do and see in this area.

Going to Murat in the Auvergne region before heading to Correze is, in my opinion, an interesting choice, rather off the beaten track for the basic "Rick Steves" traveler, and a very good idea if you enjoy cycling and hiking!

Another excellent idea is to stay east of the Dordogne Valley near Brive-la-Gaillarde, where there's just as much to see and do instead of joining the crowds of tourists that invade Sarlat and its surroundings (But still, be sure to avoid Rocamadour!)
I highly recommend the Saturday morning farmers' market in Brive. One of the best in France. You'll need to arrive early to find a parking spot not too far away.

Here's another map for you, covering the Quercy / Lot / Dordogne regions:

https://www.google.com/maps/d/edit?mid=1OdPOg8AgsNn0Jlv1cNHkujaWv9p_Jpc&usp=sharing

Same comment as Balso, generally speaking, you'll often be taking small, winding roads. Don't underestimate the journey times. A route planner like Google Maps is very optimistic and sees this as a route a local delivery driver might take, not as part of a tourist trip.

Thanks to everyone for the replies. And those google maps are fantastic and very useful, thank you!

Spending four nights in the Gorges Du Tarn was mainly due to the drive time (4+hours). I figured we would likely arrive late, so that would equate to really only three days. Additionally we can leave early for Murat if we feel like it's time to move on and still have the day.

A week in Viason was due to the Gite being a weekly rental. I believe there's enough to keep us occupied there. We want to ride up Mount Ventoux, and there are the Dentelles de Montmirail, Gorges de la Nesque and the Gorges du Toulourenc to explore. Plus there is a swimming pool at the Gite...

Off the beaten track in Murat and Correze is what we like!

Near Lyon we are staying just outside of Yzeron. It's central to hikes and bike rides that the local tourist office provides: https://en.visiterlyon.com/discover/around-lyon/monts-du-lyonnais We have three nights there in what looks to be a very comfortable gite. The idea is to do some laundry, decompress, go on some walks and bike rides before the short transfer back to Lyon.

We are only spending a few days in Lyon, but that's OK with us. We've never been to Lyon, but I can only take a day or two of the larger European cities.

So we're looking forward to this (hopefully manageable) adventure in France. To be honest, I've got a little bit of that "nervous apprehension" that takes you out of the so called "comfort zone". :)

Thank you for your clarifications.
I still think that 2 full days is enough in the Gorges du Tarn area. You'll enjoy the scenic driving on the way there and out, too.
Whereas 2 full days feel tight in Corrèze, a much larger area, especially if you want to pop into nearby Périgord.
But it's not a big deal either!

As for Yzeron, that's west of Lyon, not east. I have never been to that area.

Ahh right. East not west! I got that one wrong...