Does anyone know if there is a direct trip from the French border near Charmonix to Milan, Italy? We are looking for a train that requires no changes.
I suspect that the best you're going to be able to do is to make the drop on the French side of the Geneva airport and then make your way to the Cornavin station which has a no-changer down to Milan.
I don't know enough about Geneva to provide any details.
Some of the train geeks could probably come up with a better idea.
Your not going to find any direct trains from Chamonix for the simple reason that the train tracks in Chamonix are narrow gauge and the ones going to Milan are standard gauge. Best bet might be to take the Mont Blanc Express train to Martigny then change to a Euro Cities train direct to Milan. Even between Chamonix and Martigny you still have to change trains at the Swiss border.
Check this link Chamonix>Milan. It's from the rome2rio.com website and shows potential routes and costs.
Happy travels!
There is no direct train from Chamonix. There is one from Paris, Lyon, Chambery, or Modane to Milan. See my reply to your earlier question at https://community.ricksteves.com/travel-forum/france/travel-by-car-in-france.