Funny, I never thought of the Third Man as European noir, in part because its so British.
If we include British films, than we include a lot of movies- so much so that I think the difference between Hollywood noir and European noir is illusory. Lots of Sci-Fi, for instance, is done in Europe as are lots of action flicks.
When I think European Noir- I usually think French, German, Italian. I admit, i have trouble deciding if Smilla's Sense of Snow is European Noir (as there is so much of Denmark in the film) or Hollywood- given the nature of its cast and the style of film.