I live in Europe especially Germany. I do know Geocaching and of course the game is known here. If you don't have a GPS device with a European card in it you can use your mobile phone as long you have the geocaching app. Before your son goes to Europe just with that mobile phone, make sure he looks for geocaches in areas he will be first and download the map and the cache itself. Even if you don't have an Internet connection they can use it via GPS. I did it in USA and it has worked great. He can download more when he has wifi access in a hotel for example.
We don't feel us disturbed if kids looking for caches. The opposite is the case. Adults doesn't look at kids that much when they are playing. The best cache finders are kids and dog owners
I just can say let them do it!!