Now here's the hard part: doing a synopsis without spoilers. The plot is so finely crafted, so filled with small but crucial elements, that saying anything about it beyond generalities risks ruining it. The first scene takes place in the Cote d'Ivoire and follows a young man delivering a goat to an apartment building. The next scene is set on a snowy plateau in rural France where an abandoned car is found. And that's all that's safe to say. The story follows a handful of characters whose seemingly separate lives are invisibly linked in ways that will result in a murder. The delicate architecture of the plot and the economy with which it's told are breathtaking. But this film doesn't succeed just because of its engineering; it's not simply a technical exercise in misdirection and clue-finding like an Agatha Christie story in which the characters are merely pieces on a chessboard. These people are linked, and in some cases doomed, by their extreme need for different kinds of love, and the film, using only a few deft, narrative strokes, sketches in the causes of their heartache.
Several reviews I've read have comparted its plot structure to Rashomon, which is somewhat misleading. Kurosawa's film looked at one event from the perspective of various characters, each of whom saw it differently as filtered through their memory and moral point of view. This film shows a series of events as seen by different characters. They all see exactly the same things, but they don't fully realize what they're looking at. Is the story farfetched? Yes, definitely. But that's what's required in a film of this type, it's what makes them so audaciously entertaining. And, like the best mystery films, Only the Animals saves one of it's most stunning reveals for the very last scene.