The problem is crossing the border via train.  It's not impossible, but it seems to take a lot of time.  But I would suggest looking at 

http://www.covoiturage.fr/
http://www.e-covoiturage.ch/index.php/fr/

When I lived in Annecy there was a bus that went directly to the St. Exupery airport every day.  It took about an hour to get there.  If you have a way to get to Annecy, you could catch the bus from there. 

Hey Rekka it's only 2 hours, it's because there's no direct flight from Geneva to where I want to go that's why! :-)

Jean Jacques, the covoiture is actually the best idea, don't know why I didn't think of that sooner! The problem is that the bus or the trains all require ridiculous amounts of changes which means that it wouldn't be saving me any time going there. I'm going to check it out!

Thanks guys! Have a good weekend

yes, with a car.  But the original poster doesn't have a car.  I was talking about trains

2 hours train to Lyon Part Dieu, then there s direct Tramway to the airport ( 20 min)

In case you still need info. 

I went from Lyon's airport three weeks ago. I went by direct train at 7:29 from Geneva, no problem with any security control at Cornavin station (no control, no queue), maybe because of the early departure time.

Then in Lyon, as Tryky wrote, there is a direct tram from Part Dieu to the airport but during my trip, there was a service interruption so I used compensatory shuttle bus. I was at the airport at about 10:10.