Happy Family (IMDB page) is a 2017 animated movie from Germany, about a family that gets turned into monsters by a witch. It looks like a mashup of The Addams Family, The Munsters, and Hotel Transylvania.
Warner Bros. funded the production, and are distributing it in Europe and Latin America, presumably to be followed by direct-to-DVD sales in the U.S. in 2018. It's based on a book by David Safier.
Is it furry? Well, the family includes a kid who's a wolf-boy, there are talking bats, and VAMPIRES! (Boo.)