The film starts towards the end of her life, then goes back to the beginning, then sort of jumps back and forth between her ascent to fame in her youth and her declining health in her later years. It's interesting, because it sort of works its way backwards and forwards at the same time, which allows it to focus on the peak of her life about 3/4 of the way in, then stay there for awhile to watch things begin to fall apart, and then goes back to her deathbed and indulges in a few flashbacks. At times it gets somewhat maudlin, working the picturesque childhood angle a bit too hard, but for the most part, it packs a powerful punch, emotionally. It allows the music to speak for itself, for the most part - and if listening to Edith Piaf sing doesn't make your heart clench, then you might not have one - and rarely leans too much on the "her music was so great because she poured her life into it" trope.
What's curious though, is that what I happened to particularly notice in this film is the way that the cuts from scene to scene worked. This isn't something I have ever particularly noticed before, and I'm not sure what it says about the film that it jumped to my attention this time. It started early on, when I noticed how certain shapes would kind of be echoed between cuts, so, for instance, a ball of flame in the left corner would become a patch of flowers in a field after the cut, thus keeping a kind of formal continuity in the geometric arrangement of shapes on the screen from take to take. Sometimes, it was a different kind of continuity - for example, a scene would end with Piaf talking about a watch, and then suddenly, the next scene would start with a close-up of a large clock. I don't really know what to make of that, but I found it interesting. I also noticed that there are a lot of shots of characters' reflections in mirrors, which, aside from being a nice framing device, which, for instance, in brothel scenes, called to mind famous odalisque paintings, is also a nice metaphor for lifewriting.
Also, the ending of the film was a stroke of sonic genius. The film ends with Piaf performing Je ne regrette rien, which might seem somewhat cliche but actually manages to work well, and then just cuts to dead silence and the credits. Its incredibly striking - a really beautiful kind of elegy to the chanteuse. After what seems like an eternity, a very quiet, subtle piano picks up, but still, you're left with this powerful feeling of silence at the end of a truly monumental life. Quite powerful.
Finally, though I suppose it's obvious, Marion Cotillard is absolutely incredible. A truly epic performance. Her face is just amazing, as are her gestures - she really embodies the subject. I wonder what she'll do next, honestly, because it seems like one of those roles that could easily end an actresses career. We shall see.