We spent several weeks cycling through France, but we mostly camped. Camping was not all that cheap at 20-25 Euros. The least expensive room we got was 24 Euros. It was raining, we were lost and when I asked the price she originally said, "45 Euros". She gave us a sympathetic look, reconsidered (she did not speak English, and my French sucks) and gave it to us for 24- if we used our own sleeping bags. No breakfasts are provided, at least where we stayed. However, some had kitchens available. The cheaper hotels were in the range of 45-60 Euros, and usually had some kind of breakfast.
Try a search on these:
Maison d'hôtes;
Chambres d'Hotes; and
Gites- This is the sign we saw the most. Small and inconspicuous.
We used booking.com in several European countries when we wanted to see what is available and the prices.
Pretty nice for 24 Euros!