I am just back from Italy, Switzerland and France ( I drove as my daughter was starting Uni in Italy). Might be different if you are flying.
If you are double vaccinated, very little issues, but you need to complete passenger locator forms.
In France, the NHS app is accepted everywhere with proof of vaccine. I downloaded the Tout Covid app and managed to get my vaccine certificate on that. Mask wearing is compulsory and you will be asked for your Pass Sanitaire everywhere ( especially if you wish to eat inside). Apart from that, no issues.
The Swiss were only interested in a Vignette( motorway toll pass) to get into the country. Didn't even ask for proof of vaccine, but then we had downloaded the PLF and had my car registration number, so Don't know if they knew already. Masks are compulsory.
Italy, you need an LF done no later than 48 hours before you arrive in the country. We drove to Basel Airport and got one done there. If you aren't double vaccinated you need to self isolate for 5 days. I know it's probably different if you are flying , but we weren't even stopped at the Italian border ,despite driving a British car. However fines are heavy if you don't have it. Again PLF form. You need your proof of vaccine or negative Covid test to get in absolutely everywhere. Bars, museums, restaurants ( unless eating outside), trains, buses etc etc. You do need masks. NHS QR code app works fine. We went to IKEA in Italy to get my daughter stuff and in the restaurant they had 2 huge security guards wanting to see your Covid Green pass before you were allowed to sit down. Masks compulsory. Italians Carry their Masks on their arm.
Biggest kerfuffle was getting back into UK 
. Had to have a negative lateral flow ( Calais have loads of walk in places), which was checked before we got on the ferry, and had to provide proof of day 2 PCR test booked before they let you on.