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1540s, "to dash, plunge, flop," perhaps from Scandinavian (cf. dialectal Swedish flunsa "to plunge," Norwegian flunsa "to hurry," but first record of these is 200 years later than the English word), said to be of imitative origin. Spelling likely influenced by bounce. Notions of "anger, impatience" began to adhere to the word 18c. Related: Flounced; flouncing. As a noun, from 1580s as a motion.
"wide ruffle," 1713, from Middle English frounce "pleat, wrinkle, fold" (late 14c.), from Old French fronce "line, wrinkle; pucker, crease, fold," from Frankish *hrunkjan "to wrinkle," from Proto-Germanic *hrunk-. Influenced in form by flounce (v.).