1590s, "a Norwegian," from obsolete Dutch Noorsch (adj.) "Norwegian," a reduced form of noordsch "northern, nordic," from noord "north" (see north). Also in some cases borrowed from cognate Danish or Norwegian norsk. As a language of the north (spoken and written in Norway, Iceland, etc.), from 1680s. Old Norse attested from 1844. An Old English word for "a Norwegian" was Norðman. As an adjective from 1768.
In Old French, Norois as a noun meant "a Norse, Norseman," also "action worth of a man from the North (i.e. usually considered as deceitful)" [Hindley, et. al.]; as an adjective it meant "northern, Norse, Norwegian," also "proud, fierce, fiery, strong."
c. 1200, "an inhabitant of Normandy; one of the mixed Scandinavian-Frankish people who conquered England in 1066," late Old English, from Old French Normanz, plural of Normand, Normant, literally "North man," from a Scandinavian word meaning "northman" (see Norse), in reference to the Scandinavian warriors who overran and occupied the region of France south of the English Channel in 10c. and largely adopted the customs and language of the French.
As an adjective from 1580s. As the name for a round-arched style of medieval architecture developed in Normandy and employed in England after the conquest, it is attested from 1797. Norseman "a native of ancient Scandinavia" (1817) is not historical and appears to owe its existence to Scott. Norman-French for "the form of French spoken by the medieval Normans (and preserved until modern times in English law)" is from c. 1600.