Something you might try on your exploratory trip is looking on the Gites de France website for B&Bs (chambres d'hotes) which you can rent by the night (gites rent only by the week). Find some places that have four or five rooms so that there will be other guests, hopefully mostly French. Be sure to go to breakfast every morning when the other guests do. We have learned a lot about France at the breakfast table among, most of the time, French people. We speak enough French to understand the conversations and sometimes even contribute, and often there's someone who can translate a sentence that we don't understand.
You will meet people from different parts of France and you can ask them about the town or region they live in. After a few days at the same BNB, your hosts will be quite chatty. They will probably not have much time to spend with you because running a B&B is a lot of work but they will be interested in you and help you make connections.
The French value fidelity so if/when you do pick a village or small town to stay in, decide on your favorite bakery and then go there every day, even if you wind up throwing out a hunk of bread each night. Return to the same restaurant, go to the weekly market and buy strawberries from the same seller, buy cheese from the same seller every week. Ask for advice and make every transaction a conversation.
If you're doing some research online, the French Yellow Pages/pagesjaunes can give you a sense of how lively the town is. How many boulangeries does it have? Is there a cinema? Laundromat? What brand of supermarket and how big is it? ATM? Pharmacy? Decent restaurant?
If you can find a French-English conversation group, you'll make connections there.
We're familiar with a lot of small towns in two particular areas, and few of them, though great little towns, would provide what you are looking for in a 3-month stay. One I can think of is La Ferte Bernard, population 9000. It has a train station, some excellent restaurants, an attractive church, a lively lunch/tea room/brocante, historic buildings, nice stores, bars, and two markets a week. A river runs through the town in small channels, which always makes a town interesting in my opinion.