How can I say "girl" in archaic English?
You could call her a maiden or maid or lass.
I would go with damsel, or maybe a wench (but it can also be associated with “prostitute”, so…).
Gel, but it's lower class talk. (hard G)
Don't replace “girl”, just because it doesn't sound like you'd expect early ME to sound. In fact, “girl” has been in use since the Middle English period, which is much earlier than what you're going for.