It's important to make a distinction between ownership and carry permits. Ownership permits allow you to own and store firearms in your home in a secure place, and take them (unloaded) to a shooting range.

Carry permits allow you to carry loaded firearms in public.

Carry permits tend to be heavily restricted, but I believe handguns are not. The UK is an exception in that gun control is significantly more onerous than any other European country and more or less bans civilian handgun ownership completely.

E.g. in Switzerland, it's trivial to get a handgun. Not any more difficult than buying a double barrelled shotgun or an AR-15 style rifle. On the other hand it's very difficult to get a license that allows you to carry loaded firearms. The regular firearm permit allows you to transport unloaded guns from your home to the shooting range and back.

There are a lot of shooting clubs in former eastern bloc countries as well, and both long guns and handguns are popular for sport shooting.