The OzFoxes FoxWeb: All About Foxes PART 1: THE TECHNICAL BACKGROUND
The fox is a canid (family Canidae), distantly akin to coyotes, jackals, and wolves; but they are a distinct and separate animal, having formed their own genetic group 11-12 million years ago. They belong to the Order Carnivora and are indeed carnivores (meat-eaters); but they also eat fruits and grains, so by diet they are more properly omnivores... but that's a matter for taxonomists.

Foxes cannot cross-breed with dogs or other canids, having a different number of chromosomes. If you see a foxy-looking dog, that's exactly what it is: a dog with foxy features, not a dog-fox cross.