Coyotes and red foxes seldom interact in the wild, as foxes tend to give coyotes a wide berth. In urban areas, however, they seem to get along just fine:
Over the years, foxes and coyotes, like so many other wild species, have settled in the city, and they’re inevitably here to stay. It’s not uncommon to see them scampering across their neighborhoods. Some animal species have adapted to thrive amid the human-dominated landscape of high rises, fragmented green space, and heavy traffic. Now, at least in the case of these two wildlife predators, they may be changing their behavioral instincts to coexist with each other—thanks in part to the abundance of food.
[A recent] study has found instances where the two species forage for food at roughly 90 m from one another without incident. And in a rarely seen moment captured in Madison by PBS for their documentary, “Fox Tales,” a vixen remains alert as a pair of coyotes scavenges alarmingly close to a den with her pups inside. Drake said the interaction happened weekly for over a month, and yet there was no attempt for the mother to move her den.
Both species seem to live pretty close to me in the Uptown neighborhood of Chicago. I've seen more than one coyote on my street. (Fortunately, while foxes may not bother them, they still run away from humans.) I'm also seeing fewer rats. So, hey, foxes and coyotes are both welcome in Chicago, as far as I'm concerned. I'm glad they're not competing.