If you think Europe=the UK then I suppose you would get that impression but no, this is false. Pretty much none of the communist parties which have any kind of real representation in Europe are trotskyist. Almost none of the ones that used to were either (for instance the French communist party or the Italian communist party, both of which were huge at some points). It's only the UK where trots were really big for some reason. In most of the rest of Europe it was either USSR aligned parties or in some places maoists/some titoists. Today the titoists are pretty much completely gone, and a number of new radical leftist parties which consist of many tendencies have sprung uo, but still trotskyists aren't big anywhere, except, again, for the UK. There isn't even a reason to be trotskyist any more, most people who were trots back in the day were trots because they didn't like the USSR. Except in most of Europe these people just went directly to socdem parties (which trots did structurally anyways) and in some places they became maoists or anarchists or whatever. I don't know if you're American or if you are from the UK and that's the reason you have a warped perception about the rest of Europe but it's just not how it is, there's very few trots left outside the anglo sphere. The only places in Europe other than the UK where they are something are Portugal where they are part of a big tent multi tendency party (except Portugal also has an old guard single tendency USSR aligned party in the Parliament) and also I guess Melenchon personally used to be a trot although that doesn't even really count and in France they are vastly outnumbered by more traditional MLs, maoists and various ultras/libertarians.

Also trotskyism is an ML faction.