In the 31st century, Ulysses travels with his companions in a spaceship, facing various challenges and encountering mythological creatures. Trying to find his way back home, Ulysses battles evil gods and explores the mysteries of the universe.

The Fenouillards (Sophie Desmarets and Jean Richard are the parents, Annie Sinigalia and Marie-José Ruíz are the daughters) are shopkeepers with higher aspirations. The Monsieur wants to run for mayor of their town, but the family acknowledges he has little experience of the real world -- and so they all take off to experience it together. After starting out by getting lost, the family goes through an odyssey that takes them to Brazil, the Antarctic, and Japan in a series of episodic adventures.

The same day of their marriage, Jean's wife dies of a strange ailment in the middle of surgery. Afflicted by the loss, the young man abandons his medical studies and takes refuge in the memories of his time of courtship. At the same time that this happens, a wave of murders shakes the city with the same pattern of behavior: the victims are surgery students whose bodies have had both hands amputated.