It looks to me as though the fox was shot with a centrefire rifle, which would be totally legal if the shooter was either employed by, or had due permission from, the land owner.
Although it's a bit late in the season it is quite possible that the dog fox was carrying the egg back to the earth where its cubs lived.
I hold no brief for the person who left the dead beast lying around in full sight. As said, at the least throw the carcass in a hedgerow or ditch.
Captivebolt.