Biopics of composers are somewhat of a staple of Hollywood (and foreign) cinema. Look at the daunting list from Wikipedia. Not surprisingly, Chopin leads the list, with Schubert second (pale, handsome romantics, desperately in love and dying young ... irresistible!).
For many critics, these films have perhaps not been the cinema's finest hours. They have been often derided as sentimental , historically inept, and wildly distorted, and their depictions of creativity as crude and reductive. These charges have most often been aimed at the main practitioner of films with composers as their focus--Ken Russell. Russell is a very complex and fascinating artist (he acted, wrote, was a photographer ... he also directed opera). Charged with willful distortion and outrageous manipulation (or is it genuine myth-making?), feverish travesties (or is it a delightfully flamboyant and highly expressive use of any theatrical means available?), derided as crude and vulgar (or truth through excess, in the manner of Blake?), Russell remains a controversial figure. Read more here.
But I would also recommend the series of very influential and often quite extraordinary programs he did for the BBC early in his career (some consider these his best work): check them out on Amazon. Let's look a few examples of his work (and others):
Chopin and Liszt:
A SONG TO REMEMBER (1945), directed by Charles Vidor
Cornell Wilde as Chopin and Merle Oberon as George Sand
MAGIC FIRE (1955), directed by William Dieterle
Alan Badel as Wagner and Yvonne de Carlo as Minna
Music arranged by Eric Korngold (who also appears as Hans Richter)
LISZTOMANIA (1975), directed by Ken Russell (incidentally, the sobriquet "Lisztomania" was created by Henrich Heine)
The following films depict the composer as rock star (literally ... Roger Daltrey of The Who plays Liszt!). Two more Ken Russells:
THE MUSIC LOVERS (1970)
And here are a few more contemporary examples.
COCO CHANEL AND IGOR STRAVINSKY (2009), directed by Jan Kounen
IMMORTAL BELOVED (1994), directed by Bernard Rose