This beautiful story about an unnamed Guy and Girl flourishes with the music they make. They only spend one week together, but you just know neither forgot each other after that.
2) Begin Again
3) Hedwig and the Angry Inch
Hedwig transitioned from a man to a woman in order to marry an American GI, however his surgery didn't go as planned so now poor Hedwig is playing her music in bars across the U.S while another boyfriend stole her songs and became famous off of them. This film is so fun and has brilliant performances.
Bonus: This Is Spinal Tap - This was actually the first film that came to mind, but since the guys that played the members of Spinal Tap actually went on tour *as* them, I wasn't sure if it counts. Because doesn't this technically make Spinal tap real musicians? I don't know. The Piano was another that came to mind because the music played in that film is so lovely.