I agree with iWill. Driving to Chamonix from Geneva beats taking the train. However I've had good luck with the airport transfer services which pick you up at the airport, along with others and take you to your destination in Chamonix. Here's a few companies to contact.
Chamonix Valley Transfers is a booking agent that works with a number of different transfer providers. They can help you find pricing and schedules to fit your needs. http://chamonix-valley-transfers.com.
Mountain Drop-Offs. http://www.mountaindropoffs.com. Phone is 00 33 450 47 17 73.
Chamonix Shuttles http://www.chamonixshuttles.com The phone number is 0033 680 90 75 06.
Transfer 2theAlps http://www.transfer2thealps.com phone is 00 33 608 52 64 26.
Cham Express is run by The Skier's Lodge in Les Houches. http://chamexpress.com. Phone number: 0033 450 54 73 72.
ACT, Andy Cleaver Transport http://www.act-chamonix.com. Phone is 00 33 450 34 40 87.
Finally, here's the transportation page from Chamonix.net http://www.chamonix.net/english/transport/index.htm
Good luck with it. I envy you.