The story
The adjective is derived from archive (“place for storing earlier, and often historical, material; material so kept, considered as a whole”, noun) + -al (suffix meaning ‘of or pertaining to’ forming adjectives). The noun is derived from archive (“to put (something) in an archive”, verb) + -al (suffix forming nouns, especially of verbal action).
Etymology from Wiktionary, CC BY-SA 4.0.