1810, from or by influence of French archaique (1776), ultimately from Greek arkhaikos "old-fashioned," from arkhaios "ancient, old-fashioned, antiquated, primitive," from arkhē "beginning, origin," verbal noun of arkhein "to be the first," hence "to begin" and "to rule" (see archon). Not merely crude, the archaic has "a rudeness and imperfection implying the promise of future advance" [Century Dictionary]. Archaical is attested from 1799.
-istic
adjectival word-forming element, from French -istique or directly from Latin -isticus, from Greek -istikos, a compound of the adjectival suffix -ikos (see -ic) + the noun suffix -istes (see -ist).