These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Also, there are actually seven books (the first one being the one made into a film). However, only the first two (and more recently, the fifth) have been translated into English.
Audience-Alienating Premise: Felidae is a film noir with blood, gore, murder, sex, and a cult. Starring cats. Its look made many people think it was a Disney-type movie, but the actual content is not kid-friendly, scaring away both kid and adult audiences. The film has since gained a cult status online, however.
Fridge Logic: Comes up between books 1 and 2. The one that hits the hardest is the Company of the Merciful vs. Jesaja. Both the Company and Jesaja live underground. The Company have gone blind from living in the darkness, but Jesaja has not. While Jesaja seems healthy enough with no sun, the Company have to sunbathe briefly every day to avoid getting rickets. It's never specified just how long Jesaja stayed underground, but the whole situation feels rather fishy.
For a story wherein genetics and selective breeding play a big part, the art style of the film makes it hard to pinpoint the breeds of the characters (though in fairness, telling a cat's breed by sight alone in real life can be tricky in many cases, as they don't show as much structural variation as dogs), and the design of some characters directly contradicts the breeds given in the books.
Moral Event Horizon: If Claudandus hadn't cross the line with Felicity's murder, then he did so with Solitaire, who was pregnant at the time. It all becomes moot as shortly after, we find out that the murders have been going on for years and many victims were young or pregnant, thus crossing the line much earlier than we had expected.
Shipping: The most popular pairing in the fandom seems to be Francis/Felicity even though Felicity is decapitated only minutes after she is introduced in the film and Francis's mate ends up being Nhozemptekh AKA "The cat who had sex with him in the movie."
Funny enough, Nhozemptekh is not even mentioned in the second book.
She is mentioned, albeit extremely briefly, towards the very end of the book. Perhaps unsurprisingly, Francis comments on all the sex he's had with her. Francis's ship for the second book is Alcina, a wildcat. She is murdered partway through the book, leaving Francis rather devastated.
Francis apparently has a fetish for undomesticated females...
Well, they are the ones that are most easily available, and least likely to be spayed.
Signature Scene: Felidae is largely known only for the very explicit, shocking, and disgusting sex scene between two minimally anthropomorphiccartoon cats. To a lesser extent, it's known for it's most gory scenes, such as the one with the disemboweled pregnant cat.
Tear Jerker: 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.
The lynx from the second book. He was brought to Germany from Canada with a group of other lynxes to repopulate the wild. However, since the Canadian lynx's primary food source, the snowshoe hare, was no longer available to them, some members of the group starved to death. A few others were shot by farmers after they attacked livestock in desperation, and the remaining lynxes eventually scattered. He's now alone, and will probably remain so for the rest of his life.
Francis. Moreso in the books, wherein the things he sees and goes through have a much more obvious effect on him - more than once he breaks down crying. (Can you really blame him?)
Jesaja. He's an old cat on the verge of losing his sanity, believing himself to be Guardian of the Dead, and is utterly crushed when he feels that The Prophet ( who is actually Pascal/Claudandus) has abandoned him. However, at the end of the novel, he is finally persuaded by Francis and Bluebeard to step into the light and is adopted by a bartender.