What do you call the chain mail around the helm? I am talking about the chain mail that's supposed to protect the lower face of an armor wearer as seen in the picture. I am pretty sure there's a generic or specific term for it.
It's an aventail:
An aventail or camail is a flexible curtain of mail attached to the skull of a helmet that extends to cover the throat, neck and shoulders.
It's not a well known term (most people would just generically refer to it as chain mail), but the word aventail does date back to Middle English.
On a similar note, the proper term for a hood of chain mail is mail coif, another term that dates back to Middle English but ultimately isn't in wide circulation today. It's not the same thing as an aventail but looks similar when a helmet is worn over it.