Sapient and savor are cognates (words with the same origin)—which shouldn’t be surprising, as they both pertain to being perceptive.
These words, and the others discussed below, derive from the Latin verb sapere, meaning “taste” or “have a flavor.” Savor, from the same Old French word, is both a noun and a verb, though the former is rare; that form refers to having a good smell or taste or to a quality that makes something enjoyable or interesting, while the verb means “enjoy for a long time.” The adjectival form, savory, means “pleasant smelling or tasting” but also applies to foods that are salty or spicy but not sweet. By extension, something savory is morally acceptable; the antonym, unsavory, is more common.
A related, though rare, term is sapid; similarly, insipid, its opposite, is more widely employed, though it is more likely to be used to mean “boring” or “dull” in reference to a person’s personality rather than “lacking in flavor.”
Savoir faire, adopted into English directly from French, stems from the French verb savoir, meaning “know”; it means, basically, “knowing the right thing to do” in the sense of acting appropriately in society. (Faire is derived from the Latin verb facere, meaning “do,” which is also the source of fact.) A similar French term, savoir vivre (literally, “knowing how to live elegantly”), likewise made its way into English but is much less well known.
A savant is “a learned person,” which is its definition in the original French. The phrase “idiot savant” was applied, starting in the late nineteenth century, to someone who has what is now referred to as savant syndrome, a condition in which a person with a mental disability nevertheless demonstrates exceptional skills in mathematics, memory, or art or music. (Idiot, ultimately from Greek, originally referred to an ignorant person but then became a classification of mental ability; it has come almost full circle in meaning.) The term savvy, which refers to practical intelligence (and is employed as a verb meaning “know” or “understand”), started out as pidgin developed in parallel from the French phrase savez-vous, meaning “Do you know?” and the Spanish phrase sabe usted, meaning “You know.”
Sapient, borrowed directly from French, means “wise”; the binomial nomenclature for the human race is Homo sapiens (literally, “human being wise”). A neologism, sapiosexual (apparently coined in the late 1990s), refers to someone attracted to highly intelligent people. Sage, descended from an Old French word spelled the same way, was originally an adjective meaning “wise” but came to be used as a noun as well to refer to a wise person.