As Jules says, back in the day to "fire" an arrow was to set fire to it so that it could be used as a signal or an incendiary warhead. The term "fire" meaning to launch a projectile from a weapon only came along much later, when firearms became common. So if you writing something set before the 17th century or thereabouts, you'd loose, shoot, or let fly an arrow (even if after you've set fire to it).