In Poland in 1968, a little girl is shown the stars in the winter sky by her mother, who identifies the Christmas Eve star. In France, a little girl is shown one of the first leaves of spring by her mother, who points out the fine veins running through.
In Poland in 1990, a young Polish woman named Weronika (Irène Jacob) is singing at an outdoor concert with her choir when a sudden downpour causes the singers to rush for cover. After Weronika holds the last note alone, she meets her boyfriend, Antek (Jerzy Gudejko), and they go to his apartment to have sex. The next day she asks her father to tell Antek she is leaving to be with her sick aunt in Kraków. She tells him that lately she feels she's not alone in the world.
Weronika travels to Kraków by train looking out at the passing landscape through a small clear rubber ball. At her aunt's house, Weronika talks about her boyfriend, then meets a friend at a concert rehearsal. As the choir rehearses, Weronika, who is watching offstage, accompanies them in her soprano voice. Afterwards, the musical director asks her to audition. Overjoyed, Weronika rushes home with the sheet music. On the way, she passes through Main Market Square, where a protest rally is in progress. One protester runs into her, causing her to drop her music folder. After retrieving the sheet music, Weronika notices a French tourist taking photos of the protestors—a young woman who looks exactly like her. Weronika smiles as she watches her double board the tourist bus that soon pulls away.
At the audition, Weronika's singing impresses the musical director and conductor, and she is later told that she won the audition. The next day, while on a trolley studying the score, Weronika notices her boyfriend Antek following on his motorbike. When they talk, she apologizes for not returning his calls, and Antek tells her he loves her. Later, while getting dressed for the concert, Weronika presses her face against a window and sees an old woman with shopping bags slowly making her way along the street. That night during the concert, while singing a solo part, Weronika collapses onstage and dies.
In Paris that day, a young French woman named Véronique (Irène Jacob), after sex with her former boyfriend, is overwhelmed with sadness, as if she were grieving. The next day, at the school where she teaches music, Véronique attends a marionette performance with her class about a ballet dancer who breaks her leg and then turns into a butterfly. She then leads her class in a musical piece by an eighteenth-century composer, Van den Budenmayer—the same piece performed by Weronika when she died. That night while driving home, she sees the puppeteer at a traffic light motioning to her not to light the wrong end of her cigarette. Later she is awakened by a phone call with no one speaking, but in the background she hears a choir singing the music of Van den Budenmayer. The next day, Véronique drives to her father's house where she reveals she is in love with someone she doesn't know, and that recently she felt she was alone—that someone was gone from her life. Back in Paris, she receives a letter containing a shoelace, which she compares to her EKG graph, and a stranger shines light on her using a mirror.
Véronique learns that the puppeteer is a children's book author named Alexandre Fabbri (Philippe Volter), whose marionette story was based on his book Libellule & Papillon. One of his other books is about a shoelace. In the coming days, Véronique reads several of Alexandre's books. When Véronique visits her father, he gives her a package addressed to her containing a cassette tape. When she's alone, she listens to the mysterious recording of a typewriter, footsteps, a door opening, a train station, and a fragment of music by Van den Budenmayer. There are also sounds of a car accident and explosion. The postage stamp on the envelope leads Véronique to a Gare Saint-Lazare train station cafe where she believes the cassette recording was made. There she sees Alexandre sitting by himself, as if waiting for her. He tells her he's been waiting for her for two days, that he's working on a new book, and that this was a kind of experiment to see if she would come to him. Angered at being manipulated, Véronique leaves and takes a taxi to a nearby hotel, After checking in, she sees Alexandre, who apparently ran after the taxi. He asks for her forgiveness, and she brings him up to her room, where they both fall asleep. During the night, they confess their feelings for each other and become lovers.
The next morning she tells him, "All my life I've felt like I was here and somewhere else at the same time." While looking at a proof sheet of photos taken on Véronique's recent trip to Poland, Alexandre notices what he thinks is a photo of Véronique, but she assures him it is not her, that she in fact took the photo—of a young Polish woman carrying a music folder. Véronique is overwhelmed by a deep sadness.
Some time later at his apartment, Véronique sees Alexandre working on a new marionette with her image. When asked about the purpose of a second identical marionette, Alexandre explains, "I handle them a lot when I perform. They get damaged easily." He shows her how to work the one marionette while the double lies lifeless on the table. Alexandre reads his new book to Véronique about two women, born the same day in different cities, who have a mysterious connection. Later that day, Véronique arrives at her father's house, stops at the front gate, and reaches out and touches an old tree. Her father, who is inside the house, seems to sense this without seeing it.
