Geneva to Zermatt is about 3 1/2 hr. Trains leaves Geneva every half an hour. You can check by going to sbb.ch.
I'll wait for the TGV experts for Paris to Geneva journey time and frequency. I suspect the combine journey will take a good part of a day, EACH WAY.
3-4 hrs is about as long a journey I personally would find enjoyable. Going in, with excitement and mountain scenary, it feels like nothing. But after skiing and looking at snow all week, the multiple hour journey is likely to feel never-ending. At least that's how I felt coming back from St Moritz to Zurich (4 hrs, wished it were 2).
Add the leg from Geneva to Paris, I suspect you'll be asking "are we there yet" for a good part of the journey.
Hate to repeat my earlier comment. By train, Paris is a long way from the mountains. Geneva is a lot closer. Maybe you'd better re-think about the train part, or at least look into the travel time to VdI to compare.