Believe it or not, I had a pet fox when I was a small child , while growing up on a farm,where there were plenty of foxes. My father found him when it was very young and I raised the fox...it lived outside (in a dog house), because it was kind'a stinky (musky,to us, anyway).It was a nice pet.

It would often hunt mice and small rodents, though we fed it other food. It's sad end came when a car ran over a chicken, and he took on a liking for our live flock. I saw my father take it for a walk, (he had a gun with him) and the fox was never seen again... by me, anyway.

I can't vouch that my red fox (Sandy) was like the ones in the wild. But, my understanding is foxes mostly hunt small rodents and rabbits. I suspect they could "take on" a full grown cat, and possibly prevail, if hungry. But, if the preferred "more docile" prey is present, I can't see why a normal, healthy fox would go after a cat that would fight back?

However, if there are Coyote's in your area...cats, small dogs... and even foxes, beware.