My cyborg theory
The most logical explanation of the movie is that La Femme was a cyborg all the time. That's how she was able to singlehanded take care of every cop that got into the house. When she got out of the closet (no pun intended) near the end after getting burnt, you can clearly see how she looks cyborg and that's the reason she could go on interacting despite her injuries. This is also explained by Sarah when telling her "they said noone survived". That means La Femme did indeed die in the car accident, but was revived into a cyborg in a French government experiment.
This cyborg was meant to become a new weapon against the ongoing suburban riots. However, the human part within her was what made the cyborg experiment to eventually backfire. Some of her stronger human feelings were still present and she got obsessed with stalking Sarah and taking over her baby.