The French side is upstairs and to the right (with your back towards the front of the airport).
We usually hire from the French side as it is loads cheaper and you get less hassle from French drivers for driving s Swiss car. However, if you do go into Switzerland on the motorway, then you will get charged something like Ä60 tax.
If you ask when you hire the car, then they give you this hand drawn map that shows you how to avoid the motorway by going through the centre of Geneva. It’s not easy, but also not that difficult.
We did the journey loads last year when skiing, shuttling mates to and from the airport.
Leaving the airport from the French side you get sent down this fenced in road for a couple of Km’s and then pop out next to the border. It is also possible to stay within France and skirt around Switzerland, but you’ll probably need a GPS, we did.