Foxes put anything and everything in their mouth, regardless of whether it is food or not

Ok the one with the trident is adorable!

For me the fox just puts it in its mouth and leaves it there forever...

Sorry, the fox just putting it in it's mouth is what I meant by "eating"

I think them putting it it's mouth is intentional. They have a special eating animation for berries & meat etc.

I wonder if they ever drop the item though? Would be pretty sad if you had to kill one to get it back

only holds in mouth. The can eat only food items (when gets hurt a bit)

I think so too. They will drop the inedible items if they can pick up some other food – berries from a bush or thrown by a player, or other food items. 

Yeah there's no way this is not intentional considering they can spawn with emeralds in their mouths

@Mac Rat did you get that info from the wiki, or did you find it in the world?

Both

They can hold any item in their mouths - but they never eat non-food items, and eventually spit them out once they come across a food item.