The Mont Blanc Express is a regional train & you don't need to have advance reservations.
When we were there, in May, we took this train from Chamonix to Martigny & back to Chamonix.
We bought our tickets on the train from the conductor. We paid cash, he wrote out a receipt & that was it.
The carte d'hote grants you free train/ bus travel anywhere between Servoz & Vallorcine.
You will have to pay for the complete journey if you want to travel between Chamonix & Martigny.
Check here for more information about
what the carte d'hote covers: http://www.chamonix.net/english/transport
Have a wonderful trip!
Edit: I forgot to mention. One needs to transfer trains in Vallorcine, whether you're traveling from Martigny to Chamonix or vice- versa.
Here are the train timetables for Chamonix < > Martigny route:
Please note: If traveling from Chamonix to Martigny, you will have to show your passport at the Swiss border.