The novel opens in Paris, early in the morning, as eleven-year-old Henrietta Mountjoy, accompanied by Miss Naomi Fisher, travel via taxi to the house of Mme Fisher, an elderly and sickly lady who for years has taken in well-off girls for a season. Henrietta is travelling to Menton, in the south of France, to spend time with her grandmother, Mrs. Arbuthnot. Henrietta that she will be spending her day with Leopold, a nine-year-old boy who is supposed to meet his mother there for the first time; Miss Fisher asks Henrietta to "be a little considerate with Leopold", and "to ask Leopold nothing". After breakfast and a nap in the salon, Henrietta awakens to find Leopold standing before her. The two young children talk about their life: Leopold explains Mme Fisher's illness and his own anticipation regarding the arrival of his mother later that day; Henrietta reveals to Leopold that her mother is dead. Even though Leopold angers Henrietta by spilling the contents of her handbag, the two children develop a rapport.
Miss Fisher leads Henrietta to Mme Fisher's room. While they are upstairs, Leopold rummages through Miss Fisher's handbag, discovering three envelopes. He disregards the first, a letter pertaining to Henrietta. The second envelope, with a Berlin postmark, is from his mother, but the envelope is empty, and he feels like Miss Fisher has "done him down." The third envelope contains a letter from Marian Grant Moody, his adoptive mother, to Miss Fisher. Besides discussing the boy's itinerary, she writes exhaustively of Leopold's delicate and rather unstable constitution, and says more than once that the boy has not had a sex education yet, so any explanation of his birth will have to be handled delicately.
Leopold returns to the first envelope concerning Henrietta, written to Miss Fisher by Henrietta's grandmother, Mrs. Arbuthnot. Referring repeatedly to her old acquaintance and present addressee as "Miss Kingfisher", she informs Miss Fisher that Henrietta is to spend the remainder of the winter with Mrs. Arbuthnot in the south of France, and should only be staying a day in Paris. The tone of the letter is manipulative: Mrs. Arbuthnot subtly chastises Miss Fisher for not visiting her, all the while asking that Henrietta be allowed to spend the day in Paris.
During this time, Henrietta is introduced to Mme Fisher in her upstairs bedroom. As Miss Fisher sits knitting, her mother and the young girl converse, Mme Fisher frequently critiquing her daughter, commenting on her own bad health, and, ultimately, discussing Leopold: Henrietta learns that Leopold's now-dead father at one time broke her daughter's heart.
Henrietta then returns to the salon and discovers Leopold going through the handbag. The section concludes with the arrival of a telegram, summarised by Miss Fisher: "Your mother is not coming; she cannot come."
"Meetings that do not come off keep a character of their own." The novel's second section shift back a decade to the story of Leopold's parents. The introductory pages of the section make clear that this the entire section is imaginary, perhaps a long and dramatic imaginative vision on Leopold's part. The section contains the information that may have been exchanged between Karen and Leopold should she have actually kept her promise to her son and arrived as scheduled that day in Paris.
Karen Michaelis, ten years or so before the day of the previous section, is sailing from her native England to visit her Aunt Violet and Uncle Bill Bent at Rushbrook, County Cork, Ireland. Karen is escaping the pressures of her recent engagement to Ray Forrestier, ambivalent about the wedding; Ray himself is on a business trip. Her time with Uncle Bill and Aunt Violet is rather uneventful and uninspiring until Uncle Bill, a nervous and socially inadequate man, tells Karen that Violet is to have surgery in the coming weeks, a procedure that could prove fatal. Back in England, Karen finds Naomi Fisher waiting for her; she has travelled to London to see to the affairs of her recently deceased aunt, and tells Karen of her engagement to Max Ebhart, whom Karen met years before during while she was one of the girls staying at Mme Fisher's house. Despite Karen's objections—she had always been afraid of Max—Naomi insists the three spend time together before Max and Naomi return home.
During a picnic, Max and Karen come close, sharing a secret touch and holding hands. Afterward, Karen resigns herself to her upcoming marriage, but before too long, the Michaelis family receives news of Aunt Violet's death, and once again things are in a state of disorder. During this chaotic time Max calls and asks to see Karen. They meet clandestinely in Boulogne and spend the day together. Max reveals that Mme Fisher believes her daughter is not good enough for him, but according to Max, Naomi is an acceptable match, simply because she is "like the furniture or the dark", comfortable and reassuring. Ultimately, however, she evokes no passion in him. Likewise, Karen confides that she does not wish to marry Ray. They part, but meet again on Folkestone pier the following Saturday, spending the remainder of the day and evening in a hotel room. Karen awakens in the middle of the night and while examining her and Max's shared circumstances, she develops a type of unconscious awareness of Leopold, despite having no clear evidence he will eventually exist, suggested by the author in second person: "All the same, the idea of you, Leopold, began to be present with her."
The following day, Max writes a letter to Naomi, explaining his relationship with and feelings for Karen. Karen implores him to rethink the revelation, specifically the unreality of the arrangement ("You and I are the dream. Go back to her". ) She tears up the letter, and they agree that while Naomi must be made aware of the affair, it is best both to write her and tell her in person. Karen's rendezvous with Max is eventually discovered by Mrs. Michaelis, and while Karen tries to explain the relationship, Mrs. Michaelis cannot understand.
Next, Karen learns through the French newspapers that Max has committed suicide, and Naomi arrives in London, where she explains the circumstances surrounding his death: after receiving his letter and informing Mme Fisher of his intentions, Naomi is quarantined by her mother, who intends to keep Naomi from seeing Max and removing any possibility of spoiling Max's chance for happiness with Karen. Max does visit Naomi, however, speaking to her of the failure inherent in his relationship with Karen: "'What she and I are' he said, 'is outside life; we shall fail.'" He is visibly distressed as Mme Fisher returns to the salon. Naomi returns to her upstairs bedroom. There is a commotion in the salon, and Naomi returns to find her mother strewn across the sofa and blood on the floor. Max has cut his own wrist, making his way out the door into the street, and dying in an alley. In the following days, Mme Fisher will observe that "it was the commendation he could not bear. I was commending him when he took his knife out." At the end of the section, Karen reveals to Naomi that she is pregnant with Max's child, and will leave for Germany to try to avoid any scandal.
The first sentence of the last section repeats the last sentence of the first: "Your mother is not coming; she cannot come." Leopold again imagines how the meeting would have gone if it had occurred. Henrietta senses Leopold's disappointment; she holds him and cries. Miss Fisher reenters the salon, informing Leopold that Mme Fisher would like to see him.
Not unlike the earlier exchange with Henrietta, the conversation between Leopold and Mme Fisher is uncomfortable and at times Mme Fisher is blunt, even cruel. She attempts to explain Karen's unique nature to the disconsolate boy, abandoning any of those delicacies requested in Marian Grant Moody's earlier letter. She explains Leopold his history, including the details of his birth, the death of his half-sibling, his adoption, and his general displacement in the world. Leopold begs to remain in the house, exclaiming, "At Spezia when I am angry I go full of smoke inside, but when you make me angry I see everything." At this point Miss Fisher returns to the room and whisks Leopold away again.
Ray Forrestier is waiting in the salon for Leopold. When the child arrives, their interaction is strained, distant, and uncomfortable. A good portion of the narrative focuses on Ray's conflicting feelings about Leopold, his marriage to Karen, the child's inescapable presence in their shared life, and Ray's own situational obligations. Ultimately, Ray and Leopold leave the house together, dropping off Henrietta at the train station on the way; the two children say their goodbyes and head off in different directions.