That depends on exactly what you want out of it. What kind of animals? And are the species just the race, or do you want an entirely new badger class?
As an example, let's say a player is inspired by Sif of Dark Souls. They want to be a wolf with a sword in its mouth. I'm going to assume magic is involved in some way and give the wolf higher intelligence and the ability to speak languages. I'll allow them to wield a weapon, even a two-handed one since wolves are medium sized, in their mouth.
Stat wise we can do a +2 Dex, and a +1 to whatever is appropriate based on the backstory. Maybe they don't care, and we can just do +1 to Str. We'll give them a bite as a natural weapon, and a once per encounter save against prone. Keen Hearing and Smell, Pack Tactics, 13 AC from natural armor and choice between perception and stealth proficiency. We can talk briefly so between us we understand the various advantages and disadvantages that come from being a quadruped and how NPCs will generally react to a talking wolf strolling into town.
Is this totally balanced? I don't know. I think it's neither too powerful or too weak, which is all I'm worried about for a personal homebrew. I'd take this approach for just about any medium or small sized animal.