[Gloin the Dark]

The Red Shoes: one of the trio of main characters is a composer (though I’m not sure whether it meets the “modern and contemporary” requirement any more).

Three Colours: Blue: not a favourite of mine (and, from the trilogy, I like Red much more) but, still, it’s a highly regarded film about a composer focused on one of their major works…

Hangover Square with this wonderful concerto macaɓre for piano and orchestra by Bernard Herrmann. But this is rather about a piano Player and not a composer.

But I think that guy composes his own concerto, doesn’t he?