In Forrest Gump (1994), Jenny sings "Blowin' In The Wind" by Bob Dylan, a song about how we don't have the answers to all life's questions. The feather also represents this idea:
Forrest Gump - Main Title (Feather Theme) Sheet Music | Alan Silvestri | Easy Guitar Tab
Music Graffiti / Forrest Gump - Robert Zemeckis
Forrest Gump Jenny cantando - YouTube
Forrest Gump Theme guitar pro tab by Misc Soundtrack @ musicnoteslib.com