It is very possible to do this. It is a day of trains and busses but there are options to that too.
Touring MSM will only take a few hours. If you start in the morning you will have about 4 hours before you need to make your way back to Paris. This is more than enough.
The first thing you should think about in your visit is the Mont Sint Michel tide. Going to the MSM website you can see the times of the high and low tides. Be aware there is a tour you can take at lower tides to walk in the sand around the exterior of MSM. It is alot of fun and worth it. Don't be sad if you cannot have high tide during your visit. This tour will make up for it. The wall of water that comes in and is legendary only happens at the highest of tides monthly.
The first option is to day the day tour from Paris. Paris City Vision offers a tour and others too that pick you up at your hotel or meeting point and take you via a tourist stop to Mont Sint Michel. This is the easiest no brain way to go but will start around 7AM and end at 21:00. There are some stops along the for breaks and touristic views. You will arrive around 11:00 with the throngs of daytrippers from Paris.
For Train schedule use the German Bahn website. Its the easiest but you cannot make reservations on French trains. Use the website The Man in Seat 61 blog/website to get information on Euro train travel. Do not use EuroRail as the ticket prices are overpriced. The train portion of your journey will start in Paris Montparnasse station. There is left luggage in the station and large lockers that can accomodate kitchen sink suitcases. I can imagine in the summer season that these can be full by mid day. There is left luggage service at the tourist center at MSM which is in the small tourist area about 2kms from the base of MSM. If you decide to use this you will have to haul everything through the quick connections. I recommend leaving all luggage at your former hotel or in the Monteparnasse station. The French train stations have virtual tours online. You will be able to walk through the stations virtually to find all your services as you need before you even set foot in France. The daytrip train plan only works if you have the train tickets purchased at Montparnasse for the whole day or online. You won't have the connection times to stand in line. All departures will have to happen around 7:30 from Montparnasse to make the first bus connections. If you leave after 10:00 from Montparnasse you will most likely have to stay at MSM or an intermediary location for an overnight. This is not a bad thing as the prices and experience of hotels can be cheaper in a small French village. If you start at 07:30 you will be back in Paris by 18:30 the same day.
The second option is to take the train to Pontorson and take the grey bus from the train station to MSM. Start at Paris Montparnasse station. Easily reached by RER or even directly from CDG by Air France bus. The trip will take about 3:30 minutes total with some changeover point. Pontorson is a small train station, yellow in color. Sit in the train cars towards the middle so you can see the station signs. You can prebook online the tickets to take you all the way to MSM. The bus takes about 15 minutes from Pontorson station to MSM. If you have the need there are some places to eat in short distance around the station. There are also some places to overnight here too. You can buy your ticket for the bus online or on the bus.
The second option is to take the train from Montparnasse to Rennes at about 2:15 minutes by direct train. Rennes is a larger station and main destination for many residents. From the Rennes station walk out the main entrance to the white bus with some blue and green lettering and design. This is the Keolis-Emeraude bus. Check their website for times and the number of the bus. They run in conjunction with the Thalys and will even wait if the trains are running late. The connection times look short but it works out. You can buy your bus ticket online or on the bus. The bus will drop you off at the base of MSM.
Return trip. About 14:00 you'll need to start working your way back to Paris. Take the bus from MSM at the same point to Rennes station. There are later busses but if you took the first train out in the morning you will have already seen everything.
Need to see that morning tide? I did and there is an option for that too. Spend the full day in Paris sight seeing and then take a train around 19:00 to Rennes or Pontorson. Stay the night at either. From Rennes you will have to take the first train to Pontorson then the first bus. You will arrive at dawn at MSM. You will have to wake early for this option. Staying at Pontorson you will also jump on the first bus. Rennes affords the best selection of hotels to choose at the best prices. Pontorson has less choices but reasonable prices. MSM has OK hotels at terrible prices. Rennes also has the best options for eating. You could also take a train on the same line to Pontorson and stay at any of the villages on the same train line to experience something more native than touristic.