You can hire a car from Geneva airport. It is possible to hire from either the French or Swiss side. It is worth comparing prices as sometimes the French side can be significantly cheaper. 

Vehicles hired from the Swiss side will have a vignette which is essential to use the motorway in Switzerland. Vehicles hired from the French side will not. You can purchase one for 40 Swiss Francs from petrol stations near to the airport or avoid the Swiss motorway network and reach France driving through Geneva centre.