The thing is that the barbarians, i.e. the Cletic, Gaulic, and Germanic tribes used longswords before the Romans, Greeks, and the rest of the civilized world. Therefore the barbarian warrior should have a sword instead of an axe or club.
By giving him a sword it can justify increasing his attack from 1 to 2 or even 3. This will help give the Barbarians a credibly threatening unit and create a real concern for the player.