I know it's not quite Europe, but it is close... The Red Sea is supposed to be a great spot for shark diving. Friends who've done it rave about it, and say there are usually loads of different sharks. A quick google indicates you can normally see hammerheads from May till mid August, oceanic whitetips (Longimanus) from mid September until the end of December, and at various times species like grey reef sharks, threshers and silky sharks. However, the best spots for these are advanced scuba divers only, due to depth and current - 40+ dives is quite a typical restriction before you can dive there. From the sounds of it, that's not a good fit for you.
However, staying with the red sea, nearer shore on some of the reefs you can see smaller sharks. You'll still need to dive to see these, but you can potentially do that as a beginner (and maybe even as part of a beginner's course). The reefs often have baby blacktip reef sharks, whitetip reef sharks, and the odd leopard shark. Oh, and loads of interesting fish, rays, turtles etc, but you did say you wanted sharks!
I can't see much about snorkelling on the red sea which allows you to see sharks, it looks to mostly be snorkelling to see interesting fish.
I've not done shark diving in Europe, but I have done some in Australia. On the dives when we saw reef sharks (which do look like "proper" sharks), they weren't in the sort of place you'd be able to see them when snorkelling. The same is true of the time I saw leopard sharks, they weren't anywhere snorkellers could go.
However, I have seen quite a lot of Wobbegong Sharks (picture below) in Australia, in places where snorkellers would be able to see them / get close. Admittedly, you'd need to be good at holding your breath, as they're normally at least 5m down, and usually hiding under an overhang during the day, but it can be done (it's easier as a scuba diver though!). So, you could always find somewhere with lots of Wobbegongs, and go snorkelling there. They don't look like "classic" sharks, but they are sharks, and I think they're fun to see!
Thinking about the rest of Europe, Malta is a popular dive base in the Mediterranean. It's very very rare to see Sharks there, so I think you're unlikely to see them in the med. I believe you can sometimes see them on the Atlantic coast of europe, but only as an experienced scuba diver, and normally only with baiting the water then going down in a cage, such as described here. As with the red sea, not a beginners option.
Otherwise, another option is to go to a big aquarium, and dive with sharks there. Most of the big ones offer a package of an introduction to scuba diving, then an escorted dive with the sharks there. Typically it's quite expensive, and it's probably not the same experience as seeing them in their natural environment, but you'll know you'll get to see them!