In reply to Rob Exile Ward:
While I've only used the Swiss side (but have done so about 100-150 times!) I seem to recall there's a French entrance as well as a Swiss one, so I guess pick up on the French side. Arrivals from destinations other than French domestics would generally be on the Swiss side so need to go through French customs (not immigration, they're in Schengen) to get there, so allow time for that.
Info here:
https://www.gva.ch/en/Site/Passagers/Acces-Transports/Plan-du-Terminal-1
It appears you probably need to show your boarding card, as access through to the French side is only allowed for passengers, not just people who walk in off the street.
It appears to be accessed by car from this obscure looking turning on the right just before the Ferny-Voltaire customs post - but don't quote me on it!
https://www.google.com/maps/@46.2506548,6.118378,3a,75y,179.12h,71.1t/data=...
It's in Google Maps as "Secteur France - Genève Aéroport - GVA, Route Douanière, Grand-Saconnex, Switzerland" but be quite careful you don't get satnavved onto the Swiss motorway instead! You'll need to divert round on the D884-D1206 rather than taking the default route.
Post edited at 17:29