La fille de nulle part / The Girl from Nowhere (2012)

Michel, a retired math teacher, has lived alone since his wife's death & occupies his time writing an essay about the beliefs that shape daily life. One day he comes across Dora, a young homeless woman, who shows up injured on his doorstep, & puts her up until she recovers. Her presence brings something new to Michel's life, but gradually the apartment becomes the site of mysterious happenings.

IMDB