France, 1935. Elsa Ludgate is a 22-year-old woman with a strange condition - whenever she feels excited or anxious, her touch generates electricity. While she has tried to keep this a secret for most of her life by preventing herself from feeling any kind of emotion, things take a turn when one night, for no apparent reason, a sting appears on her chest and she loses control over her ability, causing the bursting of a street lamp. Such an event causes her to become the point of attention of the entire town, as well as Clothilde Vaccaretti, the host of The Spectacle of the Bizarre of G. Vaccaretti, a rambling circus searching for a new attraction.
As Elsa wonders what to do now that the town might be aware of her condition, Clothilde tracks her down and invites her to become part of her circus. Elsa doubts at first but eventually decides that this might be the best option for her. She joins the circus and the adventure begins.
Feeling the pressure of being the next main attraction for the circus, Elsa spends the next weeks working on her act - The Tale of the Jellyfish Girl and meets the circus crew. Among them, there is Clothilde's father and owner of the circus, Giuseppe Vaccaretti, and Jacub Kovacs, the accordionist, whose life is saved by Elsa after an accident during a rehearsal. As Elsa begins feeling more confident in her ability and herself, she engages more with the circus life. She manages to connect with them even more during a visit to Bordeaux, where the crew is intimidated by Sergeant Chevalier, a man with a personal feud against Clothilde as she is in a relationship with a woman he was in love with.
The day of the show arrives and while Elsa is initially frightened of presenting her ability to people, with the help of Jacub she performs her act and becomes an instant hit. Elsa, finally feeling that she belongs somewhere, begins to express herself and enjoy life more.
However, this doesn't last long. One day, again, for no apparent reason, she wakes up to find that her ability is gone. The circus crew tries to be supportive, but her absence quickly affects their show, so Elsa decides to "push" herself to find a way to bring it back. Knowing that her ability depends on her emotions, she tries to use her fear to once again create electricity... which only ends in a disastrous act. People get hurt and her condition is now worse than ever, making her unable to touch anything.
As the circus tries to find a solution to her condition, they are visited by Sergeant Chevalier, who threatens to take civil action against them if they don't leave town. Feeling guilty and a liability to the circus, Elsa decides to leave the circus in the middle of the night.
The circus finds out about Elsa's leaving the next day, and after discussing their options, they are convinced that they need Elsa and that it wouldn't be fair to let her go after all she did for them. They go on her search, causing Clothilde and Giuseppe to make amends for her reckless actions, as well as having Giuseppe confront Chevalier for his bullying attitude. As Giuseppe punches Chevalier, Clothilde sends Jacub to find Elsa while the crew deals with the police.
After discovering that Elsa has left for Arcachon, Jacub tracks her down and finds her hiding on the abandoned beach near the sea. Jacub asks her to return, to which Elsa replies that she is a danger to the circus in every possible aspect and that things won't end well if she returns. Jacub tells her then that the worst thing she could do to the circus is not getting them into trouble or even hurt them physically, but to abandon them, and that if she fears things not ending well, she shouldn't end them so fast. Jacub also mentions that whatever happens, they will go through it together. As they declare their love to each other, Elsa's condition changes, and becomes able to control her powers again (as it was her fear of losing what she loves which caused the problem). Elsa and Jacub make love... and after the circus crew arrives, she decides to go with them, having finally found the place and people she belongs to.