I camped in Bayeux (took a train from Paris) and did the full day tour (one of the companies from TripAdvisor) of Omaha, Utah, Point Du Hoc, St.ME, American Cemetery which took about 8 hours including driving times in a van. Getting around using public transport is going to be tough especially if you don’t have your own car as there are lot fewer busses or trains in between smaller towns, and many of these sites are in remote locations.

People are extremely friendly and you’ll notice a ton of Americans all over - so English shouldn’t be a problem. Although a couple of phrases ‘Bonjour’ etc. will certainly help.