Here's what happened
About 15 minutes in, Sarah has arrived in the house and has settled in. She's in front of her computer with a blank page in front of her. She has told John that she wants to try writing a new story in a new genre, but she doesn't know where to start. She is looking for inspiration. She glances over at the nearby dresser and notices an egg-shaped object on top of it. This gets her thinking about what kind of person might have such an object. John had mentioned his daughter. This gets Sarah thinking about what John's daughter might be like. Everything after that is part of the story in her new book.
She creates the visit from John's daughter, changing one letter in her name so she can publish the book. She makes Julia sexually active and hints that John has orgies to add sex appeal to her book. She has already met Franck and Marcel, so she adds them to the story. The other men, who Julia sleeps with, don't require names. The swimming pool features as one of the main settings for her book because it's right outside her window as she types. She throws in the little person and the mystery about the mother to add drama. John is not necessary to the book, so Sarah cannot reach him by phone (and he doesn't return calls).
The final scene is a return to "real life": Sarah's book does include a murder but is not a murder mystery or detective story. It's more about the gap between young / old, free / repressed sexuality, French / British values etc., so John is not interested. She tells John, "Keep the book. Give it to your daughter. I've signed it for her. Ciao.". This is because Sarah's dreaming about what John's daughter might be like was the inspiration for her book. She passes by John's real daughter but of course she doesn't recognize Sarah. No-one was actually killed, so Sarah is not worried about the police. The final scene is Sarah gazing on the reality behind the inspiration for her book.