In 1874 Edinburgh, on the city’s coldest day on record, Jack is born with a heart that truly does not beat. A quick-thinking midwife named Madeleine saves his life by replacing his broken pulse with a cuckoo clock. She also sets down three vital rules for Jack to follow if he is to stay alive: never touch the clock’s hands, never lose his temper, and never fall in love. Jack’s mother decides Madeleine will raise him, and Madeleine—unable to bear children herself—embraces the role with quiet, unfailing love.
On Jack’s tenth birthday, Madeleine reiterates the rules and takes him to town for the first time, where he meets a girl named Miss Acacia and instantly falls for her. Soon after, Jack begins school and encounters Joe, a bully who is equally smitten with Miss Acacia. Joe and his gang torment Jack for years, and a brutal incident leaves Jack convinced he has harmed Joe. Madeleine, seeing him as a fugitive, helps him escape and hide.
Driven by his longing to see Miss Acacia again, Jack eventually crosses paths with Georges Méliès, a magician who is trying to operate an early film camera. Georges repairs Jack’s clock-heart and agrees to accompany him on a quest to find Miss Acacia, leading them from Scotland to Andalusia, Spain.
Their journey brings them to a traveling circus in Andalusia, where Jack tracks down Miss Acacia. Georges cautions Jack not to reveal his true identity, so he befriends her while keeping his feelings to himself. Miss Acacia hints that her heart belongs to someone from her past, a hint that, for Jack, points back to him. He finally finds a moment to reveal himself and offers Miss Acacia a wind-up key that could keep his heart beating.
Just as the possibility of a life together seems within reach, Joe appears again, intent on sabotaging their bond. He explains Jack’s three rules to Miss Acacia in an attempt to break them apart. After talking with Joe, Miss Acacia decides she cannot be the cause of Jack’s death and chooses to leave with Joe, leaving Jack to tear at the screws of his clock-heart in heartbreak.
In a carriage with Miss Acacia and Joe, Jack explains that Madeleine was imprisoned after he escaped and died not long after, with whispers claiming a broken heart as the cause. Realizing she holds the key to Jack’s survival, Miss Acacia turns back to find him, learning that Jack has returned to Edinburgh and learned what happened to Madeleine.
Miss Acacia eventually locates Jack in front of Madeleine’s grave and tries to use the key to wind his heart. He refuses, discards the key, and chooses to die. They share a kiss, and as time itself seems to halt, Jack’s fate hangs in the balance. The final image carries a song about climbing to heaven with a ladder of frozen snowflakes as the narrative comes to a close.
