From Latin 'audēre' (to dare), PIE *h₂ewd- — the same verb in Horace's 'Sapere aude' (Dare to know), Kant's Enlightenment motto.
Showing a willingness to take bold risks; impudently daring or disrespectful.
From French audacieux, from Latin audācia (boldness, daring, presumption), from audāx (bold, daring, rash), from audēre (to dare, to be bold), from PIE *h₂ewd- (to set in motion, to incite). The PIE root *h₂ewd- carried a sense of eager forward motion and desire, producing Latin avēre (to be eager, to crave) and avidus (eager, greedy) alongside audēre. In Latin, audāx could be laudatory or pejorative — boldness tips easily into recklessness — and this ambivalence passed intact into English