Le Cimetière des Chiens is in Asnières-sur-Seine, a commune in the suburbs just to the northwest of Paris proper. Don’t despair, it’s really not very far; only a 25-minute métro ride (if that) from central Paris — plenty close for you to pay a quick visit during your Parisian vacation!
While the cemetery is commonly referred to as simply Le Cimetière des Chiens, you’ll see a few places where the longer name of Le Cimetière des Chiens et Autres Animaux Domestiques (the cemetery of dogs and other pets) is given, including an inscription in stone on a monument near the entrance. So the cemetery has welcomed non-canine animals as well for a long time, perhaps since the place first opened in 1899. There are tons of cat graves, as well as some horses, at least one monkey, a sheep, a hen, etc.