Travel & Leisure points out that next year is the 80th anniversary of the D-Day invasion, so if that is in your plans, be aware that it will be even busier than usual.
A busy Normandy is all relative. Normandy—even the areas around the WWII battle zones—is very spread out and there is always somewhere to go that isn't too crowded. I would imagine it would pale in comparison to Paris during the Olympics for example. That being said, because it is relatively rural, there just aren't the number B&B or hotel rooms to accommodate everyone who wants to go during a big anniversary. If you haven't already made your reservations (I made mine two years ago) you are most likely out of luck at this point unless you are willing to drive quite a distance each day to see the sights and activities. And there will be road closures in areas where dignitaries will visit on June 6th itself. By the way, I have visited Normandy during a D-day anniversary eight times—including the 70th and 75th anniversaries.