[fi-ley, fil-ey; French fee-le]
Dictionary.com Unabridged Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018
C20: from French: net, from Old Provençal filat, from fil thread, from Latin fīlum
Word Origin and History for fileting
1841 in cookery, reborrowing from French of the same word that had been taken 14c. and anglicized as fillet (q.v.). Filet mignon is attested as a French word in English from 1815.
The 'Chateaubriand,' the 'entrecôte,' and the 'filet mignon' (of mutton), with other forms, are all due to the more enlarged sympathies of the French butcher for what is perfect. We must entirely change the mode of cutting up the carcase before we can arrive at the same perfection in form of meat purchasable, and as that is hopeless, so is it useless to insist further on the subject on behalf of the public. ["The Kitchen and the Cellar," "Quarterly Review," April 1877]
Online Etymology Dictionary, © 2010 Douglas Harper