To fall on the ground suggests he was standing on the ground in the first place, and fell over. He may have even stumbled.
To fall to the ground is to come from above, from the sky, or off a table or tree or such, and hit the ground.
However, you can get away with fell on the ground in some cases. For example, you could say that many apples had fallen on the ground - the emphasis here changes from the fall itself, to the litter of apples all around you.