The airport is on the France/Switzerland border. The main or International Terminal, Geneva Cointrin, is in Switzerland. It links internally to the Geneve Ferney terminal which is the French side of the airport (see layout).
So, it is possible to hire a car from the Swiss side or the French side of the airport. The price and choice of vehicles may differ but there are two other considerations.
It is surprisingly easy to drive through Geneva and is reasonably quick. We provide a map and advice note for each side of the airport. From the French side, the road tunnels under the runways and autoroute and down through Grand Saconnex. From the Swiss side the route from Cointrin to the lake passes directly through the commercial area and can be slow at peak times because it is constricted by tramlines, at those times it can be worth joining the other route through Grand Saconnex.
Always book car-hire ahead by internet to save time and money and get more choice. Although we give links for the individual hire companies, (unless you have a company discount) we find Holiday Autos is the best provider:
We list the companies below. Click on logo to visit their UK website. You can also find them on the airport official website but it links to French or German sites.
The Swiss side car hire desks are in International Arrivals Hall. Turn left after coming out of baggage collection/customs and they are on your right (Remember to come back here when returning the car because there are no desks in departures).
The French side car hire is a bit more complicated. Normally, after collecting baggage, turn left out of customs then left again to take the escalator up to departures (opposite car hire desks and just before UBS bank). Turn right through departures to the end and go through the French control gate (beside KLM and AirFrance desks) into the French Arrivals/Departures hall. The hire desks are each side of the exit. However, if travelling with hand-baggage only, instead of queuing at Swiss passport control it is much quicker to go up to the "transit lounge" (escalator to the left), walk through and enter the French arrivals customs that way.