I have killed several foxes with a .22 LR. Foxes are not tough like a groundhog is and any .22 bullet do the job is the range is reasonable (50 yards or less). Hollowpoints and high velocity rounds are not necessary. I usually shoot standard velocity target rounds through my .22 and it works fine.

Recently I did shoot a fox with a big rifle (a .375 Ruger), and it worked well also.