In Red Dead Redemption 2 near Mattock Pond you will find a fox. The place is right above Rhodes.
The Fox moves within the area marked on the screen below. In this area you can look for traces of it. You can possibly find the fox right away, without looking for its traces. If that happens, the fox will run away immediately.
What weapon to hunt the Fox with?
You can just use a bow or a gun.
Rifle - you can shoot from a long distance from a rifle; one accurate shot will be enough.
Shotgun - using the shotgun you will kill the fox right away.
Bow - just set yourself at the right distance and aim at the animal's head, if the shot is accurate, you will kill it right away.
Gun - a few accurate shots will kill the Fox.
What does the fight with the Fox look like?
The fox will not attack you, and will immediately start running away. The animal will be scared of shots, steps, and even the scent of the hero. So, you have to stay away from the fox so you don't frighten it.
What can I do with the Fox pelt?
If you go to the Trapper you can create:
Legendary Fox Moccasins - you need fox pelt and 40 dollars,
Legendary Buck & Fox Range Gloves - you need fox pelt and 28 dollars.