Traveling around France, small town and villages, is it possible these days to find lower priced places to stay without a reservation?
Lower priced than what?
$60/2 versus $100 per night
You might see a Chambres d'hotes (rooms offered in private homes) in the villages you are stopping that would have a room for that night.
If you can find airbnb's in your price range in the towns you are visiting, I would book the room now rather than trying to chance finding a place that meets your criteria and has vacancies. Searching for a place to sleep last minute could be an exercise in futility.
When will you be traveling? High season? In the dead of winter to a non touristy place? How particular are you when choosing a place? I find that the earlier I book something the more options I have. Since so many people book online now the early bird gets the worm. I always book places with free cancellation so I have the most flexibility if my plans change. You mention airbnbs, but you might want to check booking.com for apartment rentals as well.
$60/€50 per night is very low but outside of peak season in rural areas, you can find some very simple inns and chambres d'hôtes around that price point, especially if you are open to shared bathrooms. Maybe closer to $70 /€60 these days.
Campgrounds also are a very valid options, as most provide mobil-home or cottage style accommodation these days, and no, they are nothing like a trailer park.
If you stay in a single area for longer, rates get lower and a weekly apartment/ gîte/ campground stay for less $400 is doable.
If you are able to stretch to $80-90/€70-80, your options open a lot as that is still the typical price of en-suite 2-star hotel rooms and simple B&Bs out of coastal regions.
Booking in advance would be my advice, as the best cheap accommodation sells out early. Flexibility costs money!
Airbnb fixed fees are high, so I do not believe it is the solution here, unless you are OK to rent a room in somebody's home.