Let's start with the cliche. This one happens to be true, so believe it: Marion Cotillard is every bit as awesome as you have already heard - she doesn't act Piaf, she IS Piaf!! Not only that, but she captures and bottles the singer through her formative years as an unknown street singer forking out protection money to a pimp, through her arrogant stardom and many tragedies, to sad and embittered old age (a relative concept since Piaf died before her 50th birthday with an abused body and the appearance of a 95-year old.) If Cotillard does not win Best Actress Oscar by a country mile, it will be proof positive of the unreasonable prejudice against foreign language films by the Hollywood establishment - there has not been a finer display of acting these past 30 years.
As for the film, it has its highs. In particular, the ambiance of Piaf's early years in Normandy and Paris have been captured to a tee. There are also fine cameo moments, such as Piaf's relationship with Marcel Cerdan and the shocking footage of her alcoholism and drug abuse. But a number of scenes may leave the audience slightly baffled, other than adding padding!
The wayward timeshifts in La Vie En Rose are a trifle bizarre, though some make sense - using the imagery of Milord to pinpoint her life as a young girl in a brothel run by her cold-hearted madame of a grandmother. The script also uses the splintered brain of the dying singer to pick out a kaleidoscope of images from her past. Inevitably, a big screen biopic omits many critical moments and rewrites history for dramatic effect, but here the emphasis is strongly on building up a portfolio of evidence for the woman and the hows and whys within her background. In many cases this works well, but the difficulty comes in that there is no unifying theme on which to hang the pegs.
My advice is just to take in what you see and piece it together - the results are well worthwhile! As a character study, this is as rounded and complete as any you will find. La Vie En Rose pulls no punches and portrays its subject warts and all. Piaf was not always a likeable personality but her voice dripped with the pain and emotion. Art imitating life? Maybe....