'archfool' is an English compound formed from the prefix 'arch-' (from Greek 'arkhos' via Latin/Old French, where 'arch-' meant 'chief' or 'principal') combined with 'fool' (from Old French 'fol', ultimately from Latin 'follis').

'fool' came into English from Old French 'fol' and Middle English 'fol(e)', later becoming modern English 'fool'. The prefix 'arch-' (from Greek 'arkhos') became productive in Late Middle English and Early Modern English to form emphatic compounds (e.g., 'archbishop', 'arch-enemy'). The compound 'arch-fool' (hyphenated) appears in Early Modern/modern usage as a jocular or pejorative formation and later solidified as 'archfool' in some usages.

Originally the elements meant 'chief' + 'mad person' (i.e., a principal madman); over time the compound came to mean 'an extreme or consummate fool' and is used chiefly as a strong insult or a joking epithet.