Well, I mean with approximately 13,000 years of co-existing with foxes, there would have been attempts to domesticate them, which have failed as we can see by this astounding lack of domesticated foxes in the World.
Perhaps in the 1200s, using foxes to hunt is found to be a great pleasure to royalty, who domestic ate them in a manner similar to Fancy rats.
Uhm. Perhaps I'm reading you wrong, but it strikes me that you've gone and rather missed the content of the OP. Assuming I'm wrong, meat is.... fairly unlikely. Further, domestication is a long process, which is why top-down efforts mostly failed up to the 1950s. It's usually the peasants that get the job done from the bottom up. Fur domestication in the medieval period is more possible, but given the easy access to furs at the time, doubtful. There's just too little impetus for it, economically.
As to the OP? Well, it's not that hard to arrange, in theory. You'll never have foxes fitting into the same slot as dogs. Sheer size will simply be decisive. So dogs still end up the main animal for hunting, protection, war, etc. Tracking may be competitive, but I'd guess the size and speed of dogs would still tend to make them dominant in the field. When and if foxes do take off, though, creatures like the terrier are suddenly obsolete. Why breed down dogs when foxes are already the right size?
In mannerisms and social behavior foxes are much more like cats. I'd expect their main value would be the same as the latter - hunters of vermin - rather than fur. Think in the perspective of early agriculturalists - which is more valuable? An animal that kills rats and mice that stand between famine and plenty, or a fur coat?
Unfortunately, the existence of cats reduces the need for foxes in this role. Why try to tame a fox to do what tame cats manage already?
If we're to get domesticated fox to the same lofty station as dogs and cats, you need to avoid this question. Which means, more or less, that you need to have simultaneous domestication. So get foxes being domesticated in East Asia before the first dynasties. Probably they start out scavenging from trash piles, and things develop from there. Whichever - fox or cat - was domesticated first would tend to relegate the other to niche roles. If it happens at roughly the same time, though, you end up with two regions using two different animals. Eventually the two meet, but being rough equals one will not replace the other. They will cross into each other's territory where niche roles are open, and eventually you have the categories of activities that small dogs and cats perform in OTL, split between foxes and cats.
At first, cats will be the obvious victim of this. Domesticated foxes seem to be friendlier and more social than cats, who early on dominated the "little companion" role. In a setting like our modern world, however, this is very bad for dogs. In OTL large and medium breeds are disappearing with urbanization in favor of apartment-capable forms, and these likely would not exist in a timeline with a domesticated fox. The only small dog strongly likely to still exist in such a world would, horrifyingly, be the chihuahua.