I saw the film almost a month ago, when it was released here in Israel. I like Edith Piaf's songs very much, and the movie makes you believe that a woman who gave us those songs was the one we see on the screen. Marion Cotillard is superb in this role, her heroine is vulnerable, doomed and dignified at the same time. I don't agree with those who say her performance is melodramatic, because the singer WAS very emotional and even melodramatic (though in a perfectly natural way) in real life too (as all the biographers remark).
One thing about the movie that annoyed me a little was the switches of time frames. I understand the purpose of it. During the first 15 minutes we get to see the sickly little girl, then Edith Piaf's days of glory and' finally, her last days, when she was a tortured creature and looked like a 70-year old woman. So even while living through the singer's happiest days we never forget how it would end quite soon. But sometimes these switches seem unnecessary and distracting. The other flaw is that a viewer must be well-familiar with the singer's biography, otherwise it would be difficult for one to understand certain moments in the film.
I don't have much to say about the director's masterful work, honestly there is none. The director had the story of life, he had the music and the haunting voice of the great singer. The latter is what makes most of the emotional impact. But I would recommend this movie sincerely, Marion Cotillard's acting alone would make it worth watching, and there are other beautiful things in it as well. The movie never seems too long, and its last minutes are very emotional, when Edith Piaf is led to the stage, she can hardly walk, and then she starts to sing 'No regrets' and transforms completely.