Eevee finds its origins in generic members of the order Carnivora, among them cats, dogs, and most mammalian carnivores. In the end, Eevee just resembles the basic small carnivorous mammal blueprint, evolves into more specific forms (from the dog like Flareon to the cat-like Espeon). As such, Eevee may be based of Miacids, the ancestors of all modern carnivorans (dogs cats hyenas bears viverids mustelids skunks racoons).
In the end, Eevee is just a basal mammal