Needs qualifying more.....
If they are in open traps/snares then a 410/9mm garden gun or shotgun has a good chance, a 12ft lb air rifle is far from satisfactory, you will have a job keeping him still to get it anywhere close.
If they are in caged traps then rifles and shotguns are a health and safety issue and not for consideration, you need a pistol, 410/9mm again or .22lr is very capable, but they still run around in the cage a lot on the whole, so great care is needed.
Yes, a 12ft lb air rifle is capable of killing a fox but should not be anyones first choice!
Drowning in th