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Tear Jerker: Felidae
Given the nature of both the film and the books, how hard any potential Tear Jerker moment hits is highly subjective. One of the strongest is the story told to Francis by the lynx in the second book, and the sadfate he's resigned himself to.
Dear God....Bluebeard's murder. And to make it worse, it was his so called friend Pascal that offed him.
Though in Bluebeard's favor, it's sort of implied he survived in the film.