Neither of these two brings any specific recall as something I've seen, but the fox suggests any of the numerous "nursery tales" on the theme of "don't take help from strangers."

The usual is "small defenseless critters" facing a task (cross the river, make a long journey, etc.) and the fox offers to help. Bad things happen to the critters. (In a few variants, bad things happen to the fox.)

Numerous authors produced children's books that were "barely not plagiarism" of a few publishers' © "Mother Goose style" collections, during your gandpa's era and for a time after he appears to have been most active. If you have any records of names of authors with whom he worked, you might find more searching a few of them, since often the illustrators got little mention in the press clippings.

Spinoffs of Aesop's Fables were also quite popular, and there were numerous "almost like Aesop" books, so searching "Mother Goose" and/or "Aesop" might get you lucky - or not - when you've exhausted more direct search strings.

John