Geneva Airport
Geneva airport is unusual as it has a French & Swiss side complete with border control. It’s worth checking which side you arrive on, but most flights from the UK arrive on the Swiss side. French hire cars are not allowed on the Swiss motorway without buying a ‘Vignette’ (Swiss motorway tax disc) so I would advise hiring from the Swiss side for both reasons.
Directions out of Geneva airport - Follow Green motorway signs for ‘France’.
Directions back into Geneva airport & re-fuelling/ returning hire car
Follow signs for airport on A1 motorway, come off and follow ‘passenger’ then ‘car rental return’ or at this point to re-fuel, follow signs for ‘France’ re-fuel at Agip just before ‘World Trade Centre’. To get back to airport after re-fuelling follow Green motorway signs for ‘France’ then enter motorway (second entry) for ‘Lousanne’ and you are back on the motorway as at the start.