I have seen the movie twice and here is my interpretation of the plot.
Fifteen years before the start of the movie, the woman played by Juliette Binoche and James have an affair. They live in France. James is probably married since she sees her relationship with him as a "certified copy," not an original like his relationship with his wife. They go on a holiday to Tuscany, staying at the hotel shown at the end of the movie. The night before the day shown in the movie is the 15th anniversary of their first night there. Her son is conceived early in the relationship. Although they never marry, the affair lasts at least a year or two. After the breakup, James abandons his son.
Five years before the start of the movie, without telling James, she moves to Florence. By coincidence James visits the city shortly afterward. He happens to see her and the boy walking past his hotel window, but he doesn't recognize her. Later in the piazza, he notices her again—she is looking at a statue with the boy. Although James still doesn't recognize her, he is struck by the fact that the boy apparently loves the statue, a copy, just as much as if it were the original. This gives him the idea for a book about certified copies in art. The central theme of the book is that a copy can be just as good in some ways as the original, as evidenced by the subtitle: "Forget the original, just get a good copy."
The book is published a few months before the movie begins. She discovers the book in a bookstore and buys several copies. By this time she has moved from Florence to a town near the place where she and James vacationed 15 years earlier. She runs a local antique shop. After she hears that James is visiting her town to lecture about his new book, she contacts him to see if they might meet. Apparently they haven't seen each other in many years.
He plans to arrive the evening before his lecture, and they agree that she will meet him at his hotel. While James considers their affair to be a long-ago closed chapter in his life, her feelings for him are as strong as ever. On their "15th anniversary" she is hoping to rekindle their relationship, both romantically and sexually. But James isn't so enthusiastic. Not only does he arrive late, but he falls asleep while she is freshening up in the bathroom. Finding him asleep on the bed, she leaves and returns home.
The next morning she attends the lecture but has to leave early to get the boy something to eat. Before leaving she passes a note to James asking him to meet her at her shop after the lecture. At the restaurant, she gives the boy a book she got James to autograph, and the boy teasingly asks why she got James to write only his first name. The fact that her son had to take her last name because he was born out of wedlock is such a painful subject for her that she has to leave the table.
Later when James arrives at her shop, they act almost like strangers because they haven't seen each other in years. They apparently spoke only a few words the night before. For the moment she overlooks his rude behavior at the hotel, hoping to salvage what she can of her original plans. James suggests an afternoon ride in the country before he catches his nine o'clock train. She says, "I'll take you to a place that you might find interesting," meaning the town where they stayed 15 years earlier.
As they drive through the countryside, they start arguing about his book. From the outset it is clear that she doesn't agree with his main point. Although it seems that they are discussing art, she is really talking about their relationship. She tells him that she doesn't like copies (she never wanted their relationship to be a facsimile of the real thing). But he tells her that he thinks copies are just fine.
When they arrive at their destination, they stop at a coffee shop. She asks how he got the idea for the book. When he begins to tell her about the woman in Florence, she realizes that it was her, and at the same time she thinks, "How could you not recognize me?" Once James sees the tears in her eyes, he slowly starts to comprehend his mistake in Florence but doesn't openly acknowledge this fact to her.
After James takes a call, perhaps from his wife, Binoche says that the woman behind the counter mistook them for a married couple. As they leave the shop, they fall into a game of pretending to be married. She uses the role-playing as a way to voice her complaints to James. She tells him how difficult and frustrating it is to be a single parent. Later when they stop at a restaurant, she talks about how he hurt her feelings the night before. At this point James is fed up with the game and yells at her, even telling her that he hates her after they leave the restaurant.
They wander through the streets and end up at the hotel where they had stayed so many years before. As they sit on the front steps of the hotel, he apologizes for "fifteen years ago and five years ago". She softens and becomes more flirty. She suggests that they go look at the room where they stayed. She remembers every detail about their holiday, but James doesn't recognize the hotel or the view outside the room window. Hoping to seduce him, she lies on the bed and asks him to stay with her. Instead he goes to the bathroom to freshen up as the bell outside the window rings eight times.
Fifteen years before the start of the movie, the woman played by Juliette Binoche and James have an affair. They live in France. James is probably married since she sees her relationship with him as a "certified copy," not an original like his relationship with his wife. They go on a holiday to Tuscany, staying at the hotel shown at the end of the movie. The night before the day shown in the movie is the 15th anniversary of their first night there. Her son is conceived early in the relationship. Although they never marry, the affair lasts at least a year or two. After the breakup, James abandons his son.
Five years before the start of the movie, without telling James, she moves to Florence. By coincidence James visits the city shortly afterward. He happens to see her and the boy walking past his hotel window, but he doesn't recognize her. Later in the piazza, he notices her again—she is looking at a statue with the boy. Although James still doesn't recognize her, he is struck by the fact that the boy apparently loves the statue, a copy, just as much as if it were the original. This gives him the idea for a book about certified copies in art. The central theme of the book is that a copy can be just as good in some ways as the original, as evidenced by the subtitle: "Forget the original, just get a good copy."
The book is published a few months before the movie begins. She discovers the book in a bookstore and buys several copies. By this time she has moved from Florence to a town near the place where she and James vacationed 15 years earlier. She runs a local antique shop. After she hears that James is visiting her town to lecture about his new book, she contacts him to see if they might meet. Apparently they haven't seen each other in many years.
He plans to arrive the evening before his lecture, and they agree that she will meet him at his hotel. While James considers their affair to be a long-ago closed chapter in his life, her feelings for him are as strong as ever. On their "15th anniversary" she is hoping to rekindle their relationship, both romantically and sexually. But James isn't so enthusiastic. Not only does he arrive late, but he falls asleep while she is freshening up in the bathroom. Finding him asleep on the bed, she leaves and returns home.
The next morning she attends the lecture but has to leave early to get the boy something to eat. Before leaving she passes a note to James asking him to meet her at her shop after the lecture. At the restaurant, she gives the boy a book she got James to autograph, and the boy teasingly asks why she got James to write only his first name. The fact that her son had to take her last name because he was born out of wedlock is such a painful subject for her that she has to leave the table.
Later when James arrives at her shop, they act almost like strangers because they haven't seen each other in years. They apparently spoke only a few words the night before. For the moment she overlooks his rude behavior at the hotel, hoping to salvage what she can of her original plans. James suggests an afternoon ride in the country before he catches his nine o'clock train. She says, "I'll take you to a place that you might find interesting," meaning the town where they stayed 15 years earlier.
As they drive through the countryside, they start arguing about his book. From the outset it is clear that she doesn't agree with his main point. Although it seems that they are discussing art, she is really talking about their relationship. She tells him that she doesn't like copies (she never wanted their relationship to be a facsimile of the real thing). But he tells her that he thinks copies are just fine.
When they arrive at their destination, they stop at a coffee shop. She asks how he got the idea for the book. When he begins to tell her about the woman in Florence, she realizes that it was her, and at the same time she thinks, "How could you not recognize me?" Once James sees the tears in her eyes, he slowly starts to comprehend his mistake in Florence but doesn't openly acknowledge this fact to her.
After James takes a call, perhaps from his wife, Binoche says that the woman behind the counter mistook them for a married couple. As they leave the shop, they fall into a game of pretending to be married. She uses the role-playing as a way to voice her complaints to James. She tells him how difficult and frustrating it is to be a single parent. Later when they stop at a restaurant, she talks about how he hurt her feelings the night before. At this point James is fed up with the game and yells at her, even telling her that he hates her after they leave the restaurant.
They wander through the streets and end up at the hotel where they had stayed so many years before. As they sit on the front steps of the hotel, he apologizes for "fifteen years ago and five years ago". She softens and becomes more flirty. She suggests that they go look at the room where they stayed. She remembers every detail about their holiday, but James doesn't recognize the hotel or the view outside the room window. Hoping to seduce him, she lies on the bed and asks him to stay with her. Instead he goes to the bathroom to freshen up as the bell outside the window rings eight times.