The distance between Chicago and Minneapolis is slightly higher than the distance between Paris and Montpellier.
For those cities in France, the time travel from city center to city center is about 3 hours and half by train, with 2 stops on the way. It beats both car and air travel, since you can just to show up at the station 5 minutes before the train departs, and don't need to go through security.
Also, the cheap tickets cost less than 50 euro, and you can get between 25% and 50% discount if you are less than 25 years old.
Realistically you'll never get tickets that cheap unless you plan weeks in advance, though.
The French train system is expensive and too centralized. You'll find many examples of how great French trains are but everyone only ever talks about traveling to or from Paris. And sure, it's great and convenient for Parisians.
But when you want to connect two mid-size, non-Paris cities that are more than ~500 km apart, travel by train becomes a time-consuming and expensive affair. For instance, taking the train from Nancy to Grenoble costs about 120€ if you're lucky; it forces you to take a massive detour through Paris and change train stations there. Changing stations in Paris is stressful and takes at least half an hour - since there are no shuttles, you must take the subway (and change subway lines too!)
All in all, what should have been a 3 hour journey becomes a costly 7-8 hour ordeal, thanks to the extreme centralization of the French rail network. Many people are getting fed up with this -- carpooling across long distances is becoming popular because it can often be faster and much cheaper than rail!
Just an annecdote, it is possible to regularly get tickets that cheap if using igtv or ouigo. I was in Montpelier last month and found a ticket for 25€ to Paris.
For those cities in France, the time travel from city center to city center is about 3 hours and half by train, with 2 stops on the way. It beats both car and air travel, since you can just to show up at the station 5 minutes before the train departs, and don't need to go through security.
Also, the cheap tickets cost less than 50 euro, and you can get between 25% and 50% discount if you are less than 25 years old.