Stuttgart is a terminal type station so walk to the front of the train, turn and walk 100 feet, turn and get on the first door onto the train if you are running tight. They will hold the departure of the connecting train if a lot of people are making the connection and I suspect there will be, if it is not a big delay (10 minutes or so).
Or you could book an earlier train to Stuttgart simply clicking on the "Transfer time 8 Min" and click on earlier train to Stuttgart, and you find there is an ICE that leaves 45 minutes earlier and gives you a 55 minute connection. Time enough to stop at Mickey D's for an Egg McMuffin and a cup of coffee.
Now lets discuss this statement:
Was it scenic enough to justify the 4 extra hours of travel?
If you take the train with the 55 minute connection time, it will take 6 hours and 15 minutes to get from the center of Munich to the center of Paris. Now if you fly, it will take 1/2 hour to get to Munich airport from the center of Munich. You should arrive 2 hours before you flight departs to allow for check-in, security, walk to the gate, be at the gate at least 1/2 before departure when they start boarding. Now 1 1/2 hours flying to Paris, only 1 hour of which is actually in the air, the rest taxiing and waiting for clearance to take off, then get to the gate in Paris. Probably 15 minutes waiting until you can actually get off the plane (unless you're in 1st class). Now walk to luggage carousel and wait another 15 minutes to get your bags. Now walk to the train station and get a train 1/2 hour into central Paris, or longer to take a cab in traffic.
So it will take at least 5 hours by flying, more likely 5 1/2 to get Munich Center to Paris Center, and 6 1/4 hours by train. If you stay with the 8 minute connection itinerary, they are the same.