The movie that put director Luc Besson on the map with a big bang.
Most people know the plot by now after an American remake and a TV series, but for those few that don't ... Nikita (Anne Parillaud) is a drug addict who kills a cop in a pharmacy robbery gone wrong. She shows no remorse and is eventually sentenced to death. After the death sentence is carried out, she wakes up in a room to be informed by her handler (Tchéky Karyo, both charming and reptilian) that she can train as an assassin for her country, or die for real. She's unsurprisingly not well socially adjusted, so this doesn't always go well. Imagine a trashy and violent version of Pygmalion.
Watching it in 2017 - having first seen it in a double bill with "Point of No Return," the American remake, 23 years ago - I find it still carries some clout. It's being 27 years old has some interesting side effects: the sound track of jangly Eighties music is a bit off-putting, but on the other hand the movie no longer looks over-the-top because it's no more violent than any current action movie ... so it comes out about even.
The story is of a young woman who seriously fucked up her life, and gets to find out how much emotional damage she has to take before she's paid her debt to society. You'll feel it, because the actors (particularly Parillaud in the lead) and script are very good.