The train would be complicated: at least 2 transfers. The first at Narbonne/Perpignan and the second at Lyon and maybe a third at Bellegarde. The trip will certainly be over 8 hours with one or two possibilities.

LYS: not that many trains from the airport TGV station. More opportunities from Gare de Lyon-Part Dieu. So, you have to take the tram to go inside the city.

GVA: I would say, it is the best option with a shuttle to Chamonix @ 6pm for 30€/pers (single trip, 50€ return).

But, to catch the plane, you have to tranfer to the airport!
Not an easy trip!