He holds it sideways to keep the arrow from falling out.
Like you're supposed to when you're not using an Olympic bow with 20 lbs of shit screwed into it which either stabilizes the whole bow, or holds the arrow, etc.
@shinta:
Is his form bad? Yes.
Does it matter? Not really. It's a movie. Hunger Games is just as bad. The one where the lead character is supposed to be great at archery. Brave is one of the few that actually cared to get it right.
edit:
And before anyone says it, yes, you in fact can be all Legolas 'n shit.