The adjective recherche means “rare”, “exotic”, “of studied refinement or elegance”, or “pretentious”. As you may have guessed, this word comes from French. It’s pronounced “ruh-sher-shay” (listen to the pronunciation at Merriam-Webster).
Recherche is related to the less extravagant word research via the Old French word recercher, meaning “to seek out”. So something that’s recherche has been “sought out with care”.
The Online Etymology Dictionary mentions that the word was used “to denote obscure excellence”, often describing 19th century “food, styles, etc.” I imagine this word would be a favorite among art film critics – or at least it’d be my favorite word to describe them! ;) Nah, just some of them.