Yet another interpretation (spoilers)

Obviously, there is no one correct answer for what happens in this film. But I would like to offer one more possible interpretation.

Julie was the daughter that Sarah never had.

This the backstory: 30 years ago in Swinging London, Younger Sarah was a carefree, bohemian, passionate young woman. One of her flings got serious and she fell in love. She was an aspiring writer, so when she wrote her first novel she showed it to her boyfriend, who wanted to go into publishing. He read it and said it was not very good. "Blood and guts are what people want to read, not feelings. You should burn it and start over." On top of that, he ended their romantic relationship. This was the single biggest trauma in her life.

Younger Sarah effectively died from that trauma. She became more serious, prudish, moralistic and became Older Sarah. The young carefree woman is gone. She writes the blood and guts John recommended and it turns out to be a hit franchise, which makes her think John was right. However, she lied when she told him that she burned the first manuscript. John moves own, marries another woman and has a daughter named Julia. Older Sarah, who has still not recovered, thinks "that could have been me, I could have had a child when John. But I would have named her Julie." Another 15 years has past. John just sees Older Sarah as a bankable client who he has to keep happy because she makes him a lot of money. He leaves her out of his private life, doesn't introduce her to hid daughter. However, Older Sarah still pines for him, even though she knows he is happily married. She misses the Young Sarah.

Going to France, she tries to work out the great trauma of her life. She imagines up Julie, who is daughter of the Younger Sarah. Julie jokingly calls Sarah "Mom". Older Sarah says "It must be difficult for a mother to have a daughter sleep with another man every night." Julies says her mom doesn't mind. Younger Sarah, from Swinging London, would not have minded. Older Sarah imagines meeting Marcel's Daughter say that Julie's Mother died in "an accident," which means that the trauma of being rejected by John "killed" Younger Sarah. She imagines that Franck rejects Julie the same way that John rejected Young Sarah, and she imagines that Julie stops it, killing the man. Perhaps Franck rejected Older Sarah, and should could not stand to be rejected again and killed him. The manuscript that Julie has that her mother wrote is Sarah's first book, the only one she wrote before becoming Older Sarah. She tries to resurrect Young Sarah by seducing Marcel. And she succeeds in bringing back the Young Sarah when the book she wrote is published and another publisher approves.