The movie stays reasonably close to the facts, though there are some mayor things changed that IMO was totally unnecessary. At the same time, more could have been done with other things. I am on purpose gonna keep this all pretty vague; as I do not want to spoil anything. If you want to know about the real case, google on it. It is a very interesting thing to do.
I would definitely have liked to have seen more background about Frederic. The case of Nicholas wasn't the first time he imposed as a missing child, neither was it the last time. As if the whole story about Nicholas wasn't bizarre enough, it gets more and more bizarre if you read up on Bourdin. He truly deserves the name Chameleon; it is incredible how good this guy is at languages and in blending in. I do understand that the movie's focus was on only one of his crimes, but I think a bit more history would have made it all even more absurd. Now, you almost feel at least a bit pity for Bourdin, but that should not happen. After all, the guy was/is a very disturbed man who didn't give a *beep* about the feelings of his victims.
The overall acting was not very good. Famke Janssen made the best of it and steals the scenes when she comes in, but I was unfortunately pretty unconvinced by the lead character. The way the story unfolds was just not good enough to convince, and the characters way too shallow. Many things are there in potential, but somehow it just doesn't work. It could have been an 'edge of your seat' thriller or drama, but it simply isn't. Throughout the whole story, it just lacks something. An other reviewer used the word 'dull', and I think that's quite a good description.
All in all; an intriguing case made to a less intriguing movie.
(Ps: An interesting little fact; Bourdin himself worked as a creative consultant for this movie. )