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The director, best known for her Oscar-winning movie Lost in Translation, took the top prize after it was unanimously voted the best film of the festival by a jury.
Somewhere follows an actor whose life is transformed when his young daughter comes to stay with him, and is based on Coppola's upbringing as the daughter of film director Francis Ford, the BBC reports.
Coppola said in her acceptance speech: "Thanks to my dad for teaching me."
Quentin Tarantino, chairman of the jury, added: "This film enchanted us from its first screening."
Spain's Alex de la Iglesia won best director for his horror film The Last Circus, while Vincent Gallo was named best actor for playing an American Taliban in Essential Killing.
More: Sofia Coppola, Movies
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