It seems to me that the "european" way of telling story is very difficult to understand for the American audience. therefore, I'll try to explain some things that might seem confusing:

there is no indication why any of the persons in this film should not be real. The plot is a bit laughable (f. ex. why does the wealthy writer stay in the house with the girl? she has enough money to rent a house herself), but the story is told in a very straight way.

It is clearly told that Julie is the daughter of the publisher and a french woman, whom he had left, because he did want to stay with his wife and children in England. Julie lies twice: she says, her mother lived in Nizza (in reality, she is dead, but of course Julie likes to imagine that her mother is still alive); she says, her mother had burnt the novel she has written (which she did not, because Julie gives the manuscript to Sarah, the writer ––> the book that Sarah gives to her publisher at the end of the film is the copied manuscript of Julies mother (we see her copying it at her computer).

Julie indeed killed Franck, because he resisted her attempts to seduce him. And because she is a mentally very disturbed character, she can't control her feelings anymore. Her self- esteem is reduced to nothing when she has no sexual power. And it is very clear that she got raped by her father when she was 13, although it isn't said (the scar on Julies stomach indicates a cesarean section/ she lost her virginity when she was 13/her father is the "king of orgies")

The publishers "english daughter", named Julia, is french Julies child. Her name is Julia because she was named by her mother, Julie, not by the publisher. And even if it was him who chose the name: for him the girl might have been a second incarnation of his elder daughter.