We were in Dinard, at Hotel Reine Hortense, which does not offer A/C, on 06-08 Jul 2012. We had already bought a 240 Volt box fan at a big-box home center, for use in "chateaux" accommodations that also did not offer A/C. This hotel overlooks a shallow beach, with a view across an inlet to St. Malo.
We desperately needed the fan every night we were in Normandy and Brittany without A/C. Your mileage may vary. We bought a fan small enough to bring home in our luggage, but that's perhaps a little compulsive! We still have it. I believe there were multiple heat deaths in Western Europe that summer.
I seem to remember reading that some of the Rick Steves tours supply earplugs because of the street exposure of the selected hotels. You might ask if your hotel has any fans for guest use. And in Bayeux, think about those earplugs. Our expensive Bayeux hotel was out of town (we had a rental car), and had A/C. Nice, icy A/C, an Asian split-ductless wall-mount brand.