In reply to Jenny C:
Local tourist sites can be helpful e.g. https://en.normandie-tourisme.fr click "plan your trip" then "places to stay. Trickier to use than say booking.com but often you'll find smaller family run B&Bs etc not on the big websites. We are lucky in the UK how good the information is online. I am often struck abroad how lots of businesses etc are just not internet savvy, so the tourist board often fills in this gap for the local farmer that rents a couple of rooms.
https://www.gites-de-france.com/en has already been mentioned - though they tend to be looking for weekends and week rentals. Its common for families in France to move to half the house and rent the other half as a gite, particularly in farming areas. The last Gite we rented as the top floor of a large very old farm house. We met the host (an old guy) and glugged wine and the mother-in-law chatted away happily in French.
If there is a campsite where you're going check their website for "Chambres" which are often en-suite, though not always. The idea is you use their other facilities but they provide the bed and room. The French equivalent of a static caravan (A plastic lodge) is also very common. Self catering with 2-3 bedrooms. Our last trip in Corsica was spent entirely in either chambres or lodges at campsites - usually way cheaper than hotels and in a nicer location.
Post edited at 08:43