"stringed musical instrument, violin," late 14c., fedele, fydyll, fidel, earlier fithele, from Old English fiðele "fiddle," which is related to Old Norse fiðla, Middle Dutch vedele, Dutch vedel, Old High German fidula, German Fiedel "a fiddle;" all of uncertain origin.
The usual suggestion, based on resemblance in sound and sense, is that it is from Medieval Latin vitula "stringed instrument" (source of Old French viole, Italian viola), which perhaps is related to Latin vitularia "celebrate joyfully," from Vitula, Roman goddess of joy and victory, who probably, like her name, originated among the Sabines [Klein, Barnhart]. Unless the Medieval Latin word is from the Germanic ones.
FIDDLE, n. An instrument to tickle human ears by friction of a horse's tail on the entrails of a cat. [Ambrose Bierce, "The Cynic's Word Book," 1906]
Fiddle has been relegated to colloquial usage by its more proper cousin, violin, a process encouraged by phraseology such as fiddlesticks (1620s), contemptuous nonsense word fiddle-de-dee (1784), and fiddle-faddle. Century Dictionary  reports that fiddle "in popular use carries with it a suggestion of contempt and ridicule." Fit as a fiddle is from 1610s.
late 14c., "play upon a fiddle," from fiddle (n.); the figurative sense of "to act nervously, make idle movements, move the hands or something held in them in an idle, ineffective way" is from 1520s. Related: Fiddled; fiddling.