Geneva to Chamonix with French Issued Visa

As long as your visa is not territorially restricted (for type C visas, no other restrictive remarks other than "ETATS SCHENGEN" in the "VALID FOR" field), it is fine visa-wise.

However, United Kingdom is currently considered to be a high-risk country by the SEM. You must be vaccinated (with any WHO-authorized vaccines) to transit through Swiss territory in this case.

Unlike the EuroAirport in Basel where you could choose to exit through French immigration and customs, there is only Swiss immigration in Geneva and all Swiss Covid rules apply.

Transit from a third country considered by the SEM to be high-risk to a Schengen state

Third-country citizens holding a residence document or a visa type D for their destination country in the Schengen area are permitted to travel through Switzerland to that country. The normal requirements for entering Switzerland apply.

It is only possible to enter Switzerland from a high-risk country in order to travel on to another Schengen state for a short stay of up to 90 days if you can prove that you have been vaccinated (see “How can I prove that I am vaccinated?”). Persons under 18 may enter Switzerland if they are travelling with an adult who has been vaccinated. Otherwise the normal requirements for entering Switzerland apply.

If you have not been vaccinated, but your destination country in the Schengen area has authorised your entry for a short stay of up to 90 days, you may only enter the Schengen area by travelling directly to your destination country (i.e. you may not travel though Switzerland).

https://www.sem.admin.ch/sem/en/home/sem/aktuell/faq-einreiseverweigerung.html#2005127624

(The last paragraph just means you cannot transit through Switzerland, not that you can only take a direct flight. If another Schengen country allows such transit, Switzerland doesn't care.)

Entering through another country is perfectly fine, that's what the Schengen area is about. There are some corner cases (if it looks like you were deceptive and try to misuse a single-entry visa for an entirely different trip) but this itinerary is very common and extremely unlikely to raise concerns.

In season, you will see an entire row of shuttle operators for various French ski resorts at Geneva airport and many people on the same flight will be doing exactly whay you are doing. Your passport won't be stamped when crossing the French-Swiss border.

You do need to be aware of two issues that are not directly related to visa and immigration rules:

• You will enter Swiss customs territory and this can have an impact on what you are allowed to take with you (e.g. alcohol) as Switzerland is not a member of the EU.
• Covid-related restrictions applicable in Switzerland might differ from those applicable in France. I have no idea whether they provide for a transit exception (or what they will look like when you take your trip) but it's possible that your carrier will require additional tests or paperwork or refuse to take you to Switzerland entirely.