Kathy, I don't see how you get "iffy" from the related experiences.
You asked about London, France and Venice.
You will be able to use Apple Pay to make purchases at places which take contactless cards in all three of those.
In London that will be virtually everywhere including the Tube and buses.
In France it will be at bigger places.
In Venice it will almost everywhere.
It is very very easy to use.
The wallet isn't an issue. It holds the information that Apple needs to make the purchase, and you can look in it for records of what you've spent and various other docs you can add like boarding passes, membership cards, etc. You don't need to do anything with it at the time of purchase.
You can have many cards linked to Apple Pay (most of mine are credit cards but I do have a couple of debit cards too) and you can make one the default.
At the time of purchase hold the phone over the touchpad (doesn't need to touch - in Covid times here in England it is often the other side of a perspex/plexiglas window) and the default card will pop on screen. If that is the card you want to use identify yourself to the phone with face id or fingerprint and boom - all is done. Because there are often multiple ways to do things on a phone you can also preauthorize the Apple Pay before you approach the touchpad. Just two quick presses of the button (varies by model) opens the cards, choose the one you want, identify, and hold the phone near the touchpad and poof!.
If you want to use a different card than the default, pull away in the top step above after the Apple Pay has opened, scroll to or tap the card you want and continue. Sounds complicated - it really truly isn't, Kathy. All takes a second or two.