Clarity ends in -ity, one of the standard Latin abstract-noun suffixes, and it has the tell-tale history that goes with such words: borrowed once through French, then rebuilt closer to the Latin. English first had it about 1300 as clarte or clerte, straight from Old French, meaning brightness or splendour. The modern form appears in the early 1400s, apparently a fresh borrowing directly from Latin claritas.
That is why the word looks more Latin than French today. The root is clarus, "clear," which also gave English clear itself through the ordinary French route — so clear and clarity are the same word in two registers, the short native-feeling one and the long learned one. The original meanings, brightness and glory and fame, have all fallen away; the sense of clearness of colour, judgment or style dates from the mid-1400s.
clarity (n.) c. 1300, clarte, clerte "brightness, radiance; glory, splendor," from Old French clerte , clartet (Modern French clarté) "clarity, brightness," from Latin claritas "brightness, splendor," also, of sounds, "clearness;" figuratively "celebrity, renown, fame," from clarare "make clear," from clarus "clear" (see clear (adj.)). Modern form is first attested early 15c., perhaps a reborrowing directly from Latin. Original senses are obsolete; meaning "clearness" (of color, judgment, style, etc.) is from mid-15c. also from c. 1300