Lower Normandy is one of the major touristic centers of the area thanks to its rich historical and cultural heritage.
From Paris (Gare St-Lazare), separate train lines head to Upper Normandy (Rouen and Le Havre or Dieppe) and Lower Normandy (Caen, Bayeux, and Cherbourg, via Évreux and Lisieux).
There are frequent trains from Paris to Rouen (70 mins, EUR 19); some continue to Le Havre (2 hrs, EUR 27). Change in Rouen for Dieppe (2 hrs from Paris, EUR 25). The trip from Paris to Deauville (2 hrs, EUR 26) often requires a change at Lisieux. There are regular trains from Paris to Caen (1 hr, 50 mins, EUR 28), some continuing to Bayeux (2 hrs, EUR 31).
Taking the train from Paris to Mont-St-Michel is not easy -- the quickest way (3 hrs, 45 mins, EUR 60) is to take the TGV from Gare Montparnasse to Rennes, then take the bus. There are three trains daily but the only one that will allow you a full day on the Mont leaves at 7 AM and arrives at 10:50 AM. The other options are 8 (arriving 1 PM) and 2 PM (arriving 7).
From Caen you can take either an early morning or late afternoon train to Pontorson (2 hrs, EUR 22), the nearest station to the Mont; then it is another 15 minutes to the foot of the abbey by bus or taxi (buses are directly in front of the station).
Unless you are willing to stick to the major towns (Rouen, Le Havre, Dieppe, Caen, Bayeux, Cherbourg), visiting Normandy by train may prove frustrating. You can sometimes reach several smaller towns (Fécamp, Houlgate/Cabourg) on snail-paced branch lines, but the irregular intricacies of what is said to be Europe's most complicated regional timetable will probably have driven you nuts by the time you get there. Other destinations, like Honfleur or Etretat, require train/bus journeys.