When flying to Geneva, do we follow Swiss or French Covid rules?

According to the Q&A: Genève Aéroport & Coronavirus / COVID-19 page:

I am a passenger arriving at Genève Aéroport, can I exit from the France sector, take the customs road towards France and thus avoid Swiss measures?

Even if you go through the French sector, you will have to go through Swiss formalities on the plane as your destination is Geneva. On arrival, you can then pass through the French sector, take the customs route and reach France. You will need to ensure that you meet the conditions to enter France.

From the Swiss formalities page:

On boarding: On boarding, everyone aged 16 and over intending to enter Switzerland by air or bus must be able to show the negative result of a PCR test (performed no more than 72 hours prior to boarding) or a rapid antigen test (performed no more than 24 hours previously). If you cannot show such a test you will not be allowed to board the aircraft or vehicle. Note: For people entering Switzerland from a country with a variant of concern, the test requirement on boarding already applies to those aged 6 and over.

All international (non-French) flights to Geneva are considered as flights to Switzerland and you will enter Switzerland.

You will need to follow the Swiss customs, immigration and Covid rules in effect, which may provide certain exemptions for transit passengers. Currently, to travel to Switzerland from the UK, a PCR test with 72 hours or a rapid antigen (lateral flow) test within 24 hours is required before boarding in addition to an entry form. The Swiss government provides a travel check tool that can provide more detailed information based on your situation (nationality, residence, travel history). Exceptions exist for children under 16 and transit passengers directly departing Switzerland for another country by plane without leaving the airport or changing the means of transportation.

At present, only fully vaccinated people can enter Switzerland for non-essential purposes, including transit to a country where you are not a resident.

Note that test requirement for fully vaccinated persons (or recovered within the last four months) would be abolished from 22nd of January. But again, Covid rules change often and you should use the travel check tool near and on your departure date.

Updated information can be found on the FOPH's website, including exceptions that may apply.

Of course, French rules will apply when you enter France and they may consider you as a traveller from the UK instead of Switzerland and apply the rules particular to travellers from the UK. In that case, a PCR or antigen test within 24 hours before your first flight from the UK will be required, in addition to declaration forms.

Note that Switzerland and France can apply different definitions of e.g. fully vaccinated so you would have to check the rules of both countries.

For your return trip to the United Kingdom, Switzerland and France are not treated differently for now. In any case, for the UK, it is your travel history during the past 10 days that matters. If you are returning to the UK directly from Geneva, you will be departing from the Swiss sector of the airport and the Swiss rules at that time will still apply.