1660s as a French word in English; nativized by 1758; from French ennui, from Old French enui "annoyance" (13c.), back-formation from enoiier, anuier (see annoy). Hence ennuyé (adj.) "afflicted with ennui," and thence ennuyée (n.) for a woman so afflicted.
So far as frequency of use is concerned, the word might be regarded as fully naturalized; but the pronunciation has not been anglicized, there being in fact no Eng. analogy which could serve as a guide. [OED]