Check out Bakemono no Ko about a boy who ends up in a different world (animals) and ends up being raised by a beast. Both stubborn but adjusts & learn from each other.

But I like Wolf Children better. Also The Cat Returns, girl and animal - cats, lots of them lol

Beauty and the beast too

Or if really want to see animal-human interaction check out the series Bojack Horseman. Different feel though as it's a comedy with some drama.