Acknowledging that there is no way out of the situation, Marianne takes Max’s loaded pistol out of the glove compartment, and shoots herself in the head.
What’s interesting to note — and I did — is that this doesn’t immediately come across in the ending of the film.
In the movie, we watch Max try to escape with Marianne in a plane, but get stopped by his military colleagues.
At this point in the story, it’s entirely possible that she committed suicide because she saw no other way out for herself… but then Max finds the letter that she left that confirms that she was sacrificing herself for her husband and child.