Band popularity has a lot to do with marketing. If you are looking at the size of European countries they have just as many influential artists as the US. UK and Sweden in particular.
Artists I particularly like are Robyn (pop), The Knife (electronic/“IDM”), Fever Ray (one half of The Knife), The Cardigans (pop), Lykke Li (indie pop), iamamiwhoami (experimental electronic) Opeth (death metal), Kleerup (electronic dance), Neneh Cherry (pop/hip-hop), José González (indie pop). Note: genres aren’t particularly useful but I thought some indication of what the artist is like is better than none.
If you like Röyksopp, I’d recommend checking out Kleerup, The Knife, iamamiwhoami, Lykke Li and Fever Ray.