In reply to FockeWulf:
I did that exact same journey 6 weeks ago. You’ll need your proof of double vaccination (printed NHS QR codes are fine and were easier than fiddling with a phone). These were only asked for at Geneva customs on arrival and the airline departure desk when returning. To transit through switzerland you also needed to fill out a form on the Swiss government site which also gives you a QR code to print but nobody asked for that. Technically you are transiting through Switzerland twice, once out and then return so you need two forms that nobody will look at. You’ll also need the french declaration that someone else mentioned, but nobody asked for that either when I was there.
To enter any restaurant, or sit at a bar you’ll need to show proof of vaccination. The french TousAntiCovid app is best for that and you can scan your NHS QR codes into it.
I also had to do the pre-departure test in Chamonix but that’s been cancelled now I think.
I didn’t need to show any paperwork for the Alpybus transfer. Every transfer bus I’ve been on from Geneva to Chamonix (must be 20+ now) has never stopped at the border.
Also, get used to wearing a mask. You’ll have one on pretty much from the moment you enter the UK airport to the moment you get off the coach in Chamonix.
*Note that while many of the forms I had weren’t checked, I also didn’t have (or contract Covid). I suspect that if I had, the paperwork would have been examined a bit more thoroughly by the appropriate authorities !!