Provence villas

Here is Rick's suggested itinerary for Provence:
https://www.ricksteves.com/europe/france/provence-french-riviera-itinerary
In addition to AirBnB, try gites.com. Keep in mind that "villa" and "city" don't really go together. With a car, it doesn't really matter, though.
There is a whole lot of France in between Provence and Normandy. I recommend you do some more research on your trip, even if it's just reading this website.

Look for Vinyards and Wineries in Provence; they often have accommodations available. Although a lot of rentals want a week's booking. Gites are a good place to start, as they have more amenities such as kitchens or laundry facilities and often swimming pools.

There are several recent discussions of Provence villages. A scroll thru the forum or a search will bring them up. Here is one:

https://community.ricksteves.com/travel-forum/france/2-weeks-in-south-france-more-riviera-or-provence

Both St. Remy and L’Isle-sur-la-Sorgue make good bases if you have a car.

Here are 2 lovely places to stay in St. Remy:

https://lamaisondeline.fr/home/
https://hotelsouslesfiguiers.com/en/

Both have onsite parking, easy in/out for day trips.

Normandy is very very far from Provence.

I second gites-de-france.com. You will do best with where you want to be. Pick a town or village you like and use that as your filter. We have used them many, many times and have always been happy. You can find short-term and long-term stays and a variety of lodgings, from trailers to villas.
They have been around longer than AirBandB and I find that they are responsive and responsible.

Bonne chance!

Just fyi, Provence is a very large area, about 12,000 sq. miles. You should probably figure out which part you want to be in for your stay and day trips.

Where in Provence would you suggest. We don’t want to be isolated. My sister dreams of going to the market and cooking in the evenings.

You might try watching some YouTube videos of individual Provence villages and see which one speaks to you.
We loved St-Remy and are returning next moth.

RS has a good guide book on Provence and Riviera as well

Found this YouTube channel as I am preparing for a trip to Provence and the walking tour videos about some of the villages are amazing!

https://youtu.be/IlKDADKHhyA?si=xc4xPVuniNpImc1F

Market days in Provence vary by town. Do your homework to know if a market is held the 3-4 days you are there, wherever it may be.

Some towns highly recommended here on the forum and rightly so...St Remy de Provence, Ilse-sur-la-Sorgue, Aix-en-Provence, Roussillon, Vaison-la-Romaine, Arles...just to name a few. Definitely rent a car, get a map of the area. There are markets in some towns or others every day. I always use a Michelin paper map and look for the whole picture to plan our routes for visiting the towns. #527 is a good one for the region. It's available on Amazon.
Have fun planning!

A website to find markets by town is jours-de-marche.fr. It's got an English language option.

Another hint...Your lodging host, whether it be a hotel or BandB or gite, will probably be able to tell you which nearby towns have markets on which days, and their hours (most are mornings, some are afternoons). If you are there in the summer (July and August), some towns have night markets which are kind of like village "block parties"....market stalls, music, dancing, group tables for sharing meals. I have always missed being there for a night market...maybe someday!

Just noting Normandy....Give yourself a day for the drive from Provence to Normandy. That is another large area, so you will need to narrow it down somewhat. Most people only think of the Omaha Beach area when they say Normandy. It is over 11000 sq. miles and includes Rouen, the Route des Abbayes, Honfleur, etc., and on its border with Brittany, Mont St. Michel. Be sure to figure out what you want to see and do there as well.
Bon voyage!