In 1810, Berlin, a young poet named Heinrich von Kleist is tormented by the inevitability of death and longs to conquer it through love. He approaches his cousin Marie with a suicide pact proposal, but she refuses. Heinrich then turns to Henriette Vogel, a married woman he met at a soiree, and asks her to join him in death. Initially appalled by his suggestion, Henriette later reveals that she is dying of a terminal illness and agrees to the pact. They plan to die together in the countryside, but their trip ends in failure when Heinrich meets an acquaintance at the inn where they are staying. After being rejected by Marie once again, Heinrich returns to Henriette and convinces her to renew their pact. However, Henriette's husband Vogel returns from Paris with news that another doctor believes she may not have a tumor after all and offers to take her to Paris for further treatment. Henriette dismisses this possibility and leaves with Heinrich to die together. In the woods, Heinrich shoots Henriette dead and then attempts to shoot himself twice, but the gun fails to fire. Vogel finds their bodies and learns from Henriette's doctor that an autopsy revealed she was healthy after all; her symptoms were caused by love. The film is a dark comedy-romance that explores themes of love death and the absurdity of life.

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Some movies that have similar genres and were produced around the same time as Amour Fou include The Lobster, He's Just Not That Into You, The Proposal, (500) Days of Summer, Crazy, Stupid, Love., Begin Again.