Etymology of beret
Posted by Johannes on 1 October 2011
Beret (cap; earlier, berret) is from the diminutive form birretum of the Latin birrus (large hooded cloak). Its name derived from the red colour [burrus: red] of the wool of which it was made. Burrus is merely a transliteration of the Greek word pyrros [Gr: πυρρός] meaning red, the colour of the fire, from pyr [Gr: πύρ], fire.

In modern Greek (Romeika):
a) pyr: n. fire [Gr: πυρ]
b) pyrosvestis: fireman, fire fighter [Gr: πυροσβέστης]
c) pyrotechnima: firework, pyrotechnics [Gr: πυροτέχνημα]
d) pyrotechnurgos: pyrotechnist [Gr: πυροτεχνουργός]
e) pyromanis: pyromaniac [Gr: πυρομανής]
f) pyrolysi: pyrolysis [Gr: πυρόλυση]
g) pyrovolo: to shoot, fire, gun [Gr: πυροβολώ]
h) pyrkayia: n. fire, conflagration [Gr: πυρκαγιά]
i) beres: beret [Gr: μπερές]; loanworn
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Valentini Mellas (@Leximaniac) said
Wikipedia disagrees with you: http://en.wikipedia.org/wiki/Beret
Beret (earlier, berret) is from the diminutive form *birretum of a Latinized Celtic (Gaulish) word birrus or birrum, which was the name of a short coat with a hood. This word is probably a close relative to Old Irish berr ‘short’, Welsh byr, Breton berr ‘short’, all from Proto-Celtic *birro-.[4]
4.^ Pierre-Yves Lambert, La langue gauloise, éditions errance 1994. p. 188.