Carrie Pearson's A Warm Winter Tail is non-fiction. It's not entirely about a fox or foxes but might help you?
Dr Seuss' Fox in Sox?! There's an Eric Carle one too, with a fox.
Then of course there's Fantastic Mr Fox. Oh wait, that's not a picture book. Duh.
I can think of several with foxes as characters but not the main character, but then there are quite a few traditional stories with foxes? Foxy Loxy and Henny Penny? Isn't there a fox in the gingerbread man too?
This reminds me of a beautiful film I watched about a little girl and her friendship with a fox. It's on Netflix in the US. The Fox and the Child. If you get a chance, watch it. It's beautiful.