Probably the hat is a chaperon (that's what David has in mind). Those usually have more frills than the simple one we see here, but it's still my best guess.
I'm going through its Wiki now which looks promising, there's a sub heading called "Using the wrong hole".
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This bit is of interest for us, both concerning Gemini and the Archer:
So on Geminiman only the bourrelet is visible, while the archer has a bourrelet without cornette, leaving just the patte hanging down.
Edit: don't google bourrelet.
Edit2: I'm actually not so sure anymore about the Gemini man. It's quite easy to find examples of just the "bourrelet" without attachments. Might this be another type of hat altogether?
I'm going through its Wiki now which looks promising, there's a sub heading called "Using the wrong hole".
You are not allowed to view links. Register or Login to view.
This bit is of interest for us, both concerning Gemini and the Archer:
Quote:A padded circular bourrelet (or rondel) evolved, which sat around the head, whilst the cornette became much longer, and gradually more scarf-like in shape, until by the 1430s it was usually straight at the sides and square-ended. Especially in Italy, the cornette was sometimes dispensed with, leaving just an un-flared tubular patte fixed to the bourrelet all round and hanging down to one side of the head. Reed (see refs) calls these sack hats
So on Geminiman only the bourrelet is visible, while the archer has a bourrelet without cornette, leaving just the patte hanging down.
Edit: don't google bourrelet.
Edit2: I'm actually not so sure anymore about the Gemini man. It's quite easy to find examples of just the "bourrelet" without attachments. Might this be another type of hat altogether?