I'm going to assume that 9 days means 8 nights, so I'd recommend 5 nights in Paris and 3 in Normandy. My husband and I did a similar trip a few years ago, and here's what worked well for us.
Day 1: settle into hotel, adjust to time change, ascend the Eiffel Tower (make sure you buy tickets in advance) and walk around the Champ de Mars (sleep Paris)
Day 2: 1st day of our two-day Paris Museum Pass - Orangerie, Tuileries Gardens, Louvre, and Arc de Triomphe for sunset (sleep Paris)
Day 3: 2nd day of our two-day Paris Museum Pass - RS's "Historic Paris Walk" featuring Notre Dame and Sainte-Chapelle, RS's "Left Bank Walk" featuring Luxembourg Gardens, St. Sulpice, and Pantheon, Rodin's museum, dinner in Rue Cler (sleep Paris)
Day 4: Day trip to Reims to see the cathedral and tour champagne houses (you could do a trip to Giverny instead) (sleep Paris)
Day 5: RS's "Montmartre Walk", RS's "Marais Walk", Trocadero Gardens to see the Eiffel Tower lit up (sleep Paris)
Day 6: train to Caen, pick up rental car, drive to Bayeux. See Bayeux cathedral and Bayeux tapestry. (sleep Bayeux)
Day 7: Normandy/D-Day sights (sleep Bayeux)
Day 8: Mont St-Michel day trip (sleep Bayeux)
Day 9: open/travel day
A few notes:
-We had already been to Paris before (this was my 3rd trip, husband's 2nd), so we didn't visit Versailles on this trip because we'd already seen it. On our previous trip, we did a morning at Versailles and spent the afternoon seeing the Ile de la Cite sights. We thought that a half-day at Versailles was plenty, but if you want to spend the full day there and still see a lot of museums, I'd investigate the four-day Paris Museum pass.
-I was four months pregnant during this trip, so we definitely took it easy :)
-MSM is completely doable as a day trip. It's a long drive from Bayeux (about 1.5 hours each way), but an easy one (straight shot on a very nice highway). We didn't stay on MSM because hotels were higher than what we wanted to pay and I thought it wasn't worth the logistics hassle, but others who have stayed there may disagree.
-We only spent about 4 hours on MSM. We arrived as early as possible, beat the crowds, and were on our way home before the hoards of tourists showed up. The island was absolutely overrun when we were leaving, so I can't imagine a full day there would be enjoyable, definitely go early or late.
I hope this helps! Paris is one of our favorite places in the world. You're going to have a great trip!