Bayeaux and St. Michael

I am assuming you mean Mont St. Michel. If that is the case, there would be no accomodations you can get to on the Mont with an elevator to it. It is a long steep walk up the Mont. There are accomodations across the causeway in the town of Pontorson, and I am sure some will have ground floor rooms. (Remember that first floor in Europe usually means what we call the second floor. Ask for a ground floor room.) That being said, I would do some research about Mont St. Michel to see what to expect. There is a tram that takes you from the parking lot and visitors center across the causeway. Then you walk uphill to the Abbey, which is at the top. You can walk slowly, but it isn't a piece of cake (Last time I went up was 8 years ago, when I was 73, and before my knee replacements. It wasn't brutal, but it was pretty difficult.) If for some reason you decide not to go up, I will say that the Mont , from a distance is a truly magnificent sight, especially with some clouds and/or a bit of fog to lend a medieval air. If you stay in Pointorson and aren't lugging your suitcases, will you be okay on the uphill walk?
Alas, I can't recall accomodations or restaurants to recommend.
Best of luck!

Judy has given an overview of Mont St Michel (I, too, am assuming that is what you meant). How do you plan on getting to MSM from Bayeux? There is no train service to MSM or Pontorson.

I highly doubt you will find a hotel with an elevator on the Mont. Whether you stay on the Mont (where the hotels are in historic buildings and run on the expensive side). or on the mainland, you can always try for a ground floor request. You might want to start your search with booking.com. I tend to trust their reviews because you need to have actually stayed at the hotel to leave a review.

While you won't find a hotel on Mont Saint Michel with no stairs, there are rooms at Hôtel Les Terrasses Poulard that do not require too much climbing. There are about 15-20 steps up from the Grand Rue (right near where you enter the gate) to the hotel entrance and then there were a few internal stairs getting from reception to the room. We had two rooms total and our other room was in the annex, which involved a good deal more climbing. So you would need to make sure they book you in a room in the main building with as few stairs as possible. I will say we much preferred the annex. Our room in the main building was musty smelling and stuffy to the point where you wanted to just leave the window open all night. But the window opened onto a ground level courtyard from which someone could easily access the window.

Everything that Judy said. And trust me, I am one who normally strongly encourages people to stay on the Mont itself and not off island. But it is called "Mont" Saint-Michel for a reason (i.e., "mount"). There are steps everywhere from the moment you step inside the gate. You can certainly enjoy the view of MSM from outside the gates, and it is very pretty. But to visit MSM itself, and particularly to stay on it, you must be fairly mobile—not mountain-climbing mobile, but not elevator-mobile either.

I echo the comments about how challenging MSM is with mobility issues. If you are unable to get around easily I probably would just stay at one of the hotels along the trolley path on the mainland. The best part of staying on the island is roaming around when the daytrippers leave. Most of what there is to see requires stairs. My daughter blew her knee out playing sports a few weeks before we went to MSM. She could walk, but the pain and swelling in her knee would get worse the longer she was on her feet. She did not want to miss out on the experience of visiting the monastery, so she was determined to make it to the top. She was able to make it up the stairs and take the tour, but as soon as the tour was over she needed to go back to the room to rest until dinner time. Her experience would not have been any worse if we had stayed on the mainland because she could not explore in the late afternoon or after dinner.

None of the restaurants on the island are going to be great, but there is a good view at Les Terrasses de la Baie.

What you are trying to accomplish is an historic feat, worthy of inclusion into the Bayeux Tapestry itself...which incidentally is no longer in Bayeux until the completion of the new museum. If you are relying on trains, it is nearly 6 hours between the two locations. It is now possible to go to Mont Saint-Michel directly from Paris (Gare Montparnasse to Pontorson/MSM Station, with a short ride on the bus) but only between April - October.

That said, why not focus on another town or towns in Normandy that make for an easier short-break? Like Honfleur > Bayeux, which is only 2 hours? If you insist on seeing Mont Saint-Michel, do both days there and I would highly recommend hiring a private guide. Options abound online with a simple search for "guide-conferencier Mont Saint-Michel" and can even include private transportation to/from Paris. A note about Normandy weather in March, this may come as no surprise but it rains then. A lot. Which means lots of wet, slippery stairs, low skies and potentially foggy or low-visibility conditions. If you have the opportunity to visit another time, to make the most of the experience, that would be ideal.

Hope this helps!