Crepuscule is a fancy word for twilight, the former coming from a Latin root, the latter from Middle English. Because so many words have come into English from Latin (and from French, which brings along Latin roots indirectly), we have many near-synonyms, one from each root language, that have different connotations and usage. Typically, the word with English roots is the more basic, everyday word and the Latinate synonym has a more technical or formal flavor:
Such is the case here. Crepuscule comes from the Latin word crepusculum (“twilight, dusk”), which developed from creper, meaning “dusky” or “dark,” but also could have the figurative meaning “obscure,” “doubtful,” or “uncertain.” Use of the word in English goes all the way back to Chaucer in the late 1300s, when he used the more Latinlike spelling crepusculus. It is more than likely that the word’s use in English in later centuries was influenced by French, which settled on the spelling crépuscule and is much more frequently used than in English, since it does the double duty of both twilight and crepuscule. Like twilight, crepuscule is occasionally used figuratively to mean “a period of decline,” as in “their twilight years”:
[Queen Elizabeth II] cannot step down no matter how much she would like to. Certainly, it would make her life far more attractive in the crepuscule of life, but that is not to be.
—CNN transcript, 14 February 2002
The adjective crepuscular (“of, relating to, or resembling twilight” or “dim”) is used much more frequently in contemporary English than crepuscule.