Both the dog and the fox are of the order Carnivora, family Canidae. The dog is of the sub-family, or species, canis lupus familiarus, the fox of the sub-family canis vulpinea (the wolf is of the sub-family canis lupus lupus - genetically indistinguishable, apart from breed and family characteristics, from canis lupus familiarus).
They share a common ancestor, the progenitor of all modern canids, hesperocyonines, which looked similar to a cross between a weasel and a fox, and evolved in North America around 40 million years ago. Hesperocyonines went extinct about 15 million years ago, leaving 2 offshoots, one of which survives as the family Canidae. About 35 million years ago another dead end, the hyena-like borophagines evolved, going extinct about 2.5 million years ago. The other offshoot, canids, includes all extinct and existing species of canid, including the domestic dog. Having evolved in North America, canids crossed a land bridge to Asia about 7 million years ago, and within a million years or so had made into and throughout Europe and the African continent. DNA analysis indicates dogs evolved from wolves about 130,000 years ago, and that the sub-species peculiar to Australia are descended from African ancestors.
Fox-Dog hybrid just ain't gonna happen; while similar in many respects, the critters aren't similar enough. Among other considerations, their blood chemistries are very different, as are their basal temperatures, the dog's nominally 101.5, the fox's about 103. The normal gestation for a fox is around 7 weeks, for a dog around 9 weeks - two or three days either way being within normal variation. Dogs, wolves, jackals, and hyenas, having sufficiently similar chemistries, metabolisms, and gestations can and do interbreed, but foxes are out of the party.
And frankly, anyone who has to ask questions concerning the ins-and-outs of maintaining a one-on-one relationship with a wild or feral critter just doesn't have the qualifications to take on the task; neither you nor the critter will get any good out of the deal, and both of you likely will suffer harm. The truly unfortunate part of that is its generally the critter that suffers the most harm.
I've got some
experience with wolves and hybrids; starting about the second page of
this topic, I get into a related discussion with somebody who was considering getting one. I hope that individual thought better of that plan.