'archaise' originates from Greek, specifically the word 'arkhaios' (Greek ἀρχαῖος), where 'arkhaios' meant 'ancient' or 'old'.

'arkhaios' passed into Late Latin and Medieval Latin as 'archaicus', was reflected in French (e.g. 'archaïser'), and entered English as the verb 'archaize'/'archaise' (with -ize/-ise spelling variants).

Initially the root meant 'ancient' or 'old'; over time the derived English verb came to mean 'to make or render something archaic (old-fashioned)'.