na-adjective
Describes something old-fashioned or belonging to an earlier period, often in artistic or cultural contexts. Used as an adjectival noun.
from French archaïque
この彫刻はアルカイックな様式で作られている。
This sculpture is made in an archaic style.
古風 is a native Japanese word meaning 'old-fashioned' or 'antique', often with a positive nuance of classic elegance, while アルカイック is a loanword used more in academic or artistic descriptions of archaic styles.
古代 means 'ancient times' and is a noun referring to a historical period, whereas アルカイック is an adjective describing the quality of being archaic.
Borrowed from French 'archaïque', ultimately from Ancient Greek 'arkhaïkós'. The exact route into Japanese is uncertain, but it is used as a loanword in artistic and academic contexts.