late 14c., pagent, "a play in a cycle of mystery plays," from Medieval Latin pagina, a word of uncertain origin, perhaps from Latin pagina "page of a book" (see page (n.1)) on notion of "manuscript" of a play.
But an early sense in Middle English also was "wheeled stage or scene of a play" (late 14c.) and Klein, Century Dictionary, etc., say a sense of Medieval Latin pagina was "movable scaffold" (probably from the etymological sense of "stake"). The sense might have been extended from the platform to the play presented on it.
With unetymological -t as in ancient (adj.). In Middle English also "a scene in a royal welcome or a Roman triumph" (mid-15c.); "a story, a tale" (early 15c.); "an ornamental hanging for a room" (mid-15c.). The generalized sense of "showy parade, spectacle" is attested by 1805, though this notion is found in pageantry (1650s).