I would spend every night in Paris. However, f you do want to see the WWII beaches area of Normandy, I would leave Paris by train one morning, go on an organized all day tour, spend the night in Bayeux, and return to Paris the next afternoon, after seeing the lovely town of Bayeux, its cathedral and museum in the morning. Trying to see much of the Norman DDay sights in one day from and to Paris is an exercise in passing half the time on the train. I would skip Mont St. Michel. If you did go there however, I would go there on day 2 from Bayex and stay the night, returning to Paris on the third day out. IMO, Paris has a whole season's worth of things to see and do, so I would stay there the whole time. Seven nights is very short. I would save Normandy and Mt St Michel for another trip, where you could devote at least 4 days (5 nights) there.
Where to stay in Paris? Try the search bar above with something like "where to stay in Paris", then filter for forum, then filter for one year or less. There are numerous threads discussing this. Also, check a guidebook as well. My local public library has some to borrow, and the overall info about areas of Paris doesn't change a lot over the years. Thast will helpo you narrow things down.
Hint....Many travelers underestimate the size of France and distances between places, and even with the great train system, they underestimate travel time between locations. Just something to consider when planning one-day day trips from Paris.
Best of luck in your planning.