French visorless cap
It is esentially 
a visorless cap--but the simple design can be worn for a... [DOC] [TLE] Basque beret - definition of Basque beret by The Free Dictionary [PAR] [French bret, from French dialectal berret and from Old Provenal berret, cap, 
both ... a soft, visorless cap with a close-fitting headband and a flat or rounded top
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