From an ocean rig, a demented scientist, Krank (Daniel Emilfork), kidnaps children to steal their dreams, as he is incapable of having dreams of his own. Among them is the little brother, Denree (Joseph Lucien), of carnival strongman and former Russian[citation needed] sailor One (Ron Perlman), who sets out to rescue him with the help of a little girl named Miette (Judith Vittet), a member of a thieves' guild composed entirely of orphaned children. They delve into the world of a bio-mechanical kidnapping cult and discover the connection between the scientist and the missing Denree.
Krank is both aided and hindered by Martha (Mireille Mossé), a diminutive woman; Irvin (the voice of Jean-Louis Trintignant), a talkative brain in a tank; and six identical clones of the genius who created them all - including Krank - and has been missing for many years (all played by Dominique Pinon). They support the cult with technology as they gather children for Krank's experiments to give him dreams as without the ability to dream, he is aging rapidly. However, he does not seem to understand that by kidnapping the children, he frightens them, causing them to have only nightmares, which are worthless to him.
Conjoined twins known as the Octopus (Geneviève Brunet and Odile Mallet) control the orphan thieves in their robberies, but have become distrustful of Miette, and hire One to help the children steal a safe. The Octopus believes Miette has been holding out on them and has deserted to help One. They employ circus performer Marcello (Jean-Claude Dreyfus) to ensure Miette pays and One returns to them, and much to his own distaste he allows Miette to drown while rescuing One from the cult using a system of mind control involving trained fleas, a special serum, and a music box.
Beneath the waters Miette's last sight is that of a deep sea diver who takes her to his lair and catalogues her body. He is revealed to be a delusional paranoid, and identical to the clones except older with a beard. An accident revives Miette and she finds One and Marcello both drinking and full of sorrow in a bar. The angered Octopus has a henchman dispose of the bumbling Marcello - though he chooses not to, resenting the Octopus' control - and uses the stolen mind control system to turn One against Miette; the smallest of actions has the largest of results in a spectacular chain of events leading to the Octopus' demise instead, and One and Miette are freed to continue searching for Denree.
When a dream escapes the rig, it plants information in Miette's mind and restores some of the diver's memories, including how he once lived on the rig before he was attacked by Krank and Martha, the woman he created as a wife, and dropped into the sea. They all converge on the rig with the diver armed to destroy it and the duo to rescue Denree. Miette is almost killed by Martha before the diver arrives and shoots the dwarf in the back with a harpoon gun. Later, Miette is forced to enter a dream world to release Denree from the dream extracting machine as the diver straps himself and dynamite to the legs of the rig. In the dream world, Miette is joined by Krank, where she uses her imagination to control the dream and foil him once and for all, somehow leading to his death. One and Miette rescue all the children as the diver happens to grab some scientific papers, finally regaining his memory of who he is - the genius who created the rig-dwellers in the first place - as the clones and Irvin row away in one boat, and One, Miette, and the lost children escape in another, just before a sea bird triggers the detonation of the explosives, killing the genius and destroying the rig.
