With 3 weeks you could choose 3 different locations. For example 1 in Normandy and 2 in Brittany. By consulting any good travel guide it is not difficult to determine which area to stay in.
Instead of Airbnb, also see Gites de France, an organization that has existed since the 60s (well, before the internet and Airbnb), very popular in rural areas where you will find accommodation ranging from a single room to a castle with a swimming pool. . These accommodations are regularly visited and controlled by the organization in order to verify they match to comfort standards.
Gites de France Normandy:
https://www.gites-de-france.com/fr/search?regions=9&seed=46136bc7
Gites de France Brittany:
https://www.gites-de-france.com/fr/search?regions=13&seed=6b8cbe31