Looking for tips

You'll be about an hour away from Albi, two hours from Carcassonne, an hour from Cahors, two hours from Sarlat and other destinations in the Dordogne, an hour from the Pech Merle cave. All are worthwhile day trips, and you could spend several days in the Dordogne. Bordeaux, about three hours away, could be another overnight trip, or an overnight stop along a longer route. Barcelona is about six hours' drive from St-Antonin.

Via Michelin is a good route-planning tool for short and longer driving trips, showing alternate routes, driving times (not including stops or traffic delays so be conservative), and estimated gas and toll costs (based on assumptions you can adjust).

The "Explore Europe" link on this website offers basic info about major destinations in France and Spain. I suggest you invest in a good guidebook like a Michelin Green Guide. There's one for France as a whole, and others for Aquitaine, Midi-Pyrenees, and other (sometimes overlapping) regions for more detail. They also produce a road atlas that may be helpful for exploring especially the rural roads. Lonely Planet is another good guidebook, and the DK guide series are richly illustrated with good information about sights.

Having GPS in the car definitely helps with navigation, but should be supplemented by maps or an atlas. We loaded a Europe map in our portable GPS and brought it with us, a considerable saving over renting one with the car. Setting it for kilometers instead of miles will help synch it with the road signs you'll be seeing. Its mispronunciation of French place names can offer unexpected hilarious moments.

[Edited to move paragraphs around. I was careless with insertions.]

I recommend using ViaMichelin.com to check routings and driving distances. The latter tend to be optimistic and do not include time for stops, traffic, looking for parking, getting lost, etc.

Mont-St-Michel is not on the way from Paris to Saint-Antonin-Noble-Val. It is west of Paris. I suspect that the best way to see it would be to take the TGV from Paris to Rennes or (if car rental is available there) Dol de Bretagne, then rent a car. If that's your only destination in the area on this trip, I wouldn't want to drive the whole way, though you could do so if you're willing to spend a full day behind the wheel.

The town of Andorra is not an attractive destination. Think tacky outlet mall. The surrounding countryside is mountainous and certainly worth seeing, but you needn't necessarily go to Andorra to see it. I enjoyed the narrow-gauge Yellow Train trip through the Pyrenees. The train runs between Villefranche-de-Conflent and Bourg-Madame. Bourg-Madame sits virtually on the Spanish border, a short distance from the very picturesque Spanish hill-top town of Puigcerda. I spent several nights in Puigcerda in 2016, taking buses to some of the surrounding towns. I though La Seu de Urgell was particularly pretty.

Barcelona is a favorite of mine but can use a lot of time. If I had your timeframe and free housing in France, this is not the trip on which I would visit Barcelona.

Although I prefer Bilbao to San Sebastian, SS is nice, and the Basque Country is worth a visit. Again, to take full advantage of it requires time away from your free housing. Also check weather (especially rainfall) stats for this area. It tends to be cool and wet even in mid-summer.

I'd spend my time in France. Toulouse is workable as a day-trip but will probably require at least two visits, if not more. The round-trip drive will take about three hours. It's a very attractive city.

Albi is a top destination that will be a bit closer (RT about two hours).

Just looking at the ViaMichelin map I see quite a number of places I've heard of but never visited that will be within range for you. You can research these and see which ones sound appealing:

Cahors
Saint-Cirq-Lapopie
Figeac
Rocamadour

Rocamadour is in the Dordogne. That whole area would be one of my targets for some time away from Saint-Antonin-Noble-Val. You'd need multiple days to see the highlights; it's definitely too far to keep driving back and forth.

Another possibility is the area stretching between Montpellier and Collioure near the Spanish border on the Mediterranean. Many enticing destinations there. Carcassonne is sort of on the way.

Two other possibilities for time away would be Provence or the Riviera. I think Provence would make more sense. Not only is it closer, but I feel as if you can accomplish more there in 4 or 5 days. A car is very, very handy in Provence. It's not as critical along the Riviera, so it would be nice to see Provence on this trip since you'll have a car.

I urge you to make this a five-week trip (or longer). France is a huge country with an unbelievable number of great destinations. The more research you do, the more time you'll want to have. I spent 89 days in France this summer and only visited the eastern part of the country. I had to skip many places I'd have liked to go, including Paris.

Make sure you visit lovely Collioure on the Mediterranean coast. It is a fun town to explore and has history of the Fauvist artists.

The classic French bistro dish cassoulet comes from the Southwest. This bean-and-meat stew can be cheap filler (think school cafeteria) or fine dining with delicious additions such as confit duck leg and top sausages. You get what you pay for and seek it out only when you are very hungry. My best taste in Toulouse came with a dessert dish of prunes stewed in Armagnac (a slightly sweeter brandy.) I retired for the night very happy.
And yes, Albi is worth a visit from Toulouse, with a red-brick cathedral and a Toulouse-Lautrec museum, although much of his best work is in bigger and fancier institutions. If you head south to San Sebastian, continue a few hours drive to the city of Bilbao. There's more there than just the famous Guggenheim Museum. Using a multi-destination airline flight search function you might be able to fly home from Bilbao's international airport, saving a lot of time.

I think you underestimate driving times. There are mountains, or at least serious hill, involved. Barcelona is about 7 hours away, ok 6 of you do not stop or get lost. That's more than an overnight, though you might take a road trip.

I do not see most of the Dordogne towns on the list, or the Vezere valley, or St. Cirq. Those are closer, and very worthwhile.

Thank you for all of your great tips and advice. We will probably drop Spain off our list for this trip unless we add a week and spend additional time seeing it on our way home.

I like San Sebastian but it's best in mid-summer. The rest of the year it's mostly cold and rainy and not really at it's best. If you were to go, there is a great castle in Olite, about 20 miles south of Pamplona, that's one of my favorites.

I'd probably use the time to explore French destinations too.