The story is one of fantasy, although Balzac preferred conte philosophique, and it is indeed a tale that explores the philosophy of life as much as the somewhat mystique talisman upon which the story is based.
Raphaël de Valentin is an aspiring author who has laboured long to produce a hefty tome only to find that he can't get it published. He owes his landlady rent and teaching her daughter Pauline piano is no longer sufficient to meet his debt. He decides to leave and is given a Napoléon (a 20 Franc piece) by Pauline to help him on his way. But he gambles it and loses.
Distraught he turns to suicide. Failing to jump into the Seine he comes across a strange antique shop with a pistol in the window. He goes in to buy it, to use on himself, but encounters a mystical old man who suggests a better plan. He shows him an animal hide that he says is invested with the power to grant any wish. But in making such a pact, the bearer must understand that for every wish the hide will shrink and, ultimately, disappear. At which point the bearer will die.
Dismissing the whole thing as bunkum, Raphaël immediately makes a number of outlandish wishes and leaves. No sooner is he in the street the first of these wishes starts to materialise. And the others are soon delivered. He becomes rich, he publishes his book having bought the publishing house, and he enjoys the company of beautiful women. But the hide continues to shrink!
He encounters a beautiful but aloof woman named Foedora, whom he fails to woo, leading him eventually to humiliate her, relying on a wish to get her to love him. Each wish shrinks the hide, and despite his efforts to stop making wishes, for various reasons he fails to do so.
Having acquired everything that he desired he starts to realise that these things are actually not really important or satisfying, and after a chance encounter with Pauline at the theatre he realises that she is the person who is the most important to him. But he has only one wish left and he must use it to save Pauline.