Can I do both of these sites on a day trip from Paris?
If you're asking, can you do both of them in one day trip, the answer is no, not that I've heard of. I have assumed that by "Normandy" you're referring to the D-Day invasion battlefields.
If you're asking, can you do the battlefields and Mont St. Michele on separate days, the answer is yes, in theory. But it may not be the experience you're looking for.
Re Normandy: There are tours such as Viator and other tour providers who will pick you up in Paris and take you on a (normally) big bus, to some of the Normandy/D-Day battle sights, and drop you off back in Paris after a long day.
Re Mont St. Michele: Basically the same deal as explained above for Normandy. You'll be one of the hundreds/thousands of "day trippers that arrive on the Big Bus tours.
This is not the way most travelers here would prefer to see Normandy and Mont St. Michele.
But if that's all you have time for, technically, it's doable in two separate days, but not in one day.
Mont St Michel is wonderful but not between 11am and 5pm. As Kent said, hordes of tourists smashed in like sardines ascending the main, narrow walkway to the top. The only worthwhile way to visit Mont St Michel is to spend the night there, enjoy it from 5pm until 11am the next day. Then, it is magical.
Normandy is not a “site”. It’s a region in France the size of a US state.
You can go to Normandy or Mont St Michel in one day from Paris, but i do not recommend it. Wait until another trip when you can spend the night on Mont St Michel, and/or spend at least 3 full days in Normandy.
You said in another thread you started (asking about going to Normandy) that you bought RS France guide but didn’t have time to read it yet. It would be good to make time to read it, it will answer a lot of your questions, it explains regions, cities, sites, how to get places, how to plan your time, etc.
em,
As the others have mentioned, seeing both sites as a single day trip from Paris is not going to be possible. You can either visit the Normandy beaches OR Mont St. Michelle, but not both. Here are some examples.....
If you have the time, spending a couple of nights in Bayeux would allow a better look at the Normandy sights.
It is spelled Mont St Michel... : )
Normandy may be your shorthand for “the D-Day Beach area”, but even with that stipulation, both are too much for one day. The D-Day beaches in particular are easier with a car. Failing that, you need a pre-booked privately run (group, or private) tour that includes transportation. These book up well in advance, especially in summer. Google Maps may help you to understand the problems.