Singer Cléo Victoire embarks on a journey filled with existential dread and self-discovery after attending a tarot card reading that leaves her unsettled. The fortune teller reveals that an ominous force is looming over Cléo, exposing her to a doctor involved in a perilous undertaking. As the reading continues, Cléo is confronted with the Hanged Man card, signaling an impending negative shift in her life, and upon being asked about her health, she confirms her illness. The fortune teller then pulls the Death card, emphasizing that it symbolizes significant change rather than just mortality, yet Cléo succumbs to despair, believing doom is inevitable. In a moment of vulnerability, she seeks solace through a palm reading, but the fortune teller, unable to assist, leaves her seeking answers.
Distraught, Cléo encounters her maid, Angèle at a café, where she recounts the chilling details of her reading. Hearing Cléo's agitation and thoughts of suicide in the face of possible cancer, Angèle comforts her with a café owner providing coffee for reassurance. The two engage in some retail therapy as they shop for hats, with Cléo choosing a striking black fur hat despite Angèle's warning against wearing something new on a Tuesday. Cléo insists on taking the hat home, saying it would bring her comfort, yet they arrange for it to be sent to her residence instead.
During their taxi ride home, one of Cléo's songs plays on the radio, reigniting her anxiety as news of the Algerian War fills the airwaves. They have an enlightening discussion with their female taxi driver about the perils she faces on the job. However, as they near Cléo's home, she becomes nauseated, attributing this to her illness. Upon their arrival, Angèle advises Cléo not to disclose her condition to her lover as “men hate illness.” When her lover arrives, he expresses his busy schedule and only manages to spare a kiss, failing to acknowledge Cléo's unspoken fears about her health.
Once he departs, Cléo is joined by Bob, a pianist, and Maurice, a songwriter, for rehearsal. They attempt to lighten the mood by jokingly pretending to be doctors, but Cléo isn't amused. As they practice, a dark cloud looms over Cléo's spirits as she performs "Sans toi," which resonates deeply with her fear of death. Confidently, she remarks that while she is spoiled, true love is scarce, prompting her to leave abruptly.
Her journey continues as she ventures into town, where a street performer captivates her attention with an unusual act. At a café, Cléo plays her song on the jukebox but is dismayed to see it elicits no reaction from her surroundings. Shortly after, she visits Dorothée, an old friend who is modeling nude for sculptors. They share contrasting views on body image, and during their heartfelt conversation, Cléo confides her anxiety about her medical results.
At the cinema, they watch a silent comedy that features Jean-Luc Godard and Anna Karina, culminating in a poignant moment where a comedic turn of events lightens the mood after Karina's character seemingly meets her end. However, as they leave, Cléo inadvertently breaks a mirror, interpreting it as a sign of misfortune related to an unfortunate event she later hears about at a nearby café.
With the day winding down, she decides to return to Parc Montsouris, where she meets Antoine, a sensitive soldier on leave from the war. He imparts a pensive reflection on mortality, encouraging Cléo to embrace her true name, Florence. Together, they ponder the weight of illness and the futility of dying in conflict. As they decide to journey together for her hospital appointment, things take a turn when Cléo learns the results of her tests are more manageable than expected, leaving her feeling a surge of optimism. Antoine expresses his desire to stay by her side, and as they share a tender moment under the vast sky, Cléo finally feels a sense of liberation from her fear, smiling brightly into what lies ahead.
