The story takes place in the far future of the 51st Century, during the year 5053.
While visiting Luna for the festival, Viscount Albert de Morcerf and Baron Franz d'Epinay make the acquaintance of the Count of Monte Cristo, a self-made nobleman. When they part, the Count promises to visit Albert in Paris. After he arrives, he introduces himself to the most powerful families in France (the Morcerfs, the Danglars, and the Villeforts).
The general plot of Gankutsuou, while broadly the same as the novel on which it is based, changes many aspects of the source material. In the novel, the narrative arc follows the Count chronologically; in the anime, the story begins with Albert and Franz meeting the Count on Luna (which occurs, in Rome, many hundreds of pages into the book), and the Count's back story is pieced together throughout the series. The anime's plot includes supernatural elements, different fates for some characters, the disposal of several side-plots, and an altogether different ending.