I'm flying to Geneva in September (from US). If I exit the airport on the French side, have I legally entered Switzerland? I'm asking because Switzerland has different Covid restrictions than France, although (hopefully) things will have changed by September.
I'm asking because Switzerland has different Covid restrictions than France
Usually you will be exempt from Swiss requirements if you are directly transiting to another country.
Current testing and quarantine obligations in Switzerland explicitly exempt transit passengers who will only enter Switzerland to reach another country.
Of course, the PCR requirement for boarding your flight does not distinguish between passengers of different destinations. For any flight-related restrictions you will need to follow Swiss rules (unless it is a domestic French flight within the French sector).
At the moment, the PCR test requirement does not differ much between Switzerland and France, but this may change in coming months (although I think it's unlikely).
As other answers noted, you will still need to pass Swiss immigration and legally you will be in Switzerland and subject to all Swiss laws. For your specific concerns however, Switzerland currently does not impose public health measures at border for transit passengers, except those concerning air travel.
Yes, you will enter Switzerland.
Only flights from France arrive at the French sector directly. For passengers arriving on international flights (i.e. where the departure airport was not in France), there is no direct access to the French sector - you must enter Switzerland first. See the FAQ page on the airport's website:
Is it possible to exit directly from the French side when arriving on an international flight without passing through Swiss territory?
No, you must pass through Swiss territory from an international flight.
Unless you arrive on a flight from somewhere else in France you will always enter Switzerland at GVA. If you arrive from another Schengen area country you will not have to pass immigration however coming from the US you will have to pass Swiss border control. Once in the Swiss sector you can cross over to the French sector, eg. to pick up a car, or to be picked up there.
Getting directly from a plane to the French sector is only possible if your flight originated in France.
(edit: Currently the French sector is even completely closed)