fillet n.

"place (papers) in consecutive order for future reference," mid-15c., from Old French filer "string documents on a thread or wire for preservation or reference" (15c.), earlier "to spin thread," from fil "thread, string" (12c.), from Latin filum "a thread, string; thread of fate; cord, filament," from PIE *gwhis-lom, suffixed form of root *gwhi- "thread, tendon." The notion is of documents hung up on a line in consecutive order for ease of reference.

File (filacium) is a threed or wyer, whereon writs, or other exhibits in courts, are fastened for the better keeping of them. [Cowel, "The Interpreter," 1607]

Methods have become more sophisticated, but the word has stuck. Meaning "place among the records of a court or office" is from 1510s; of newspaper reporters sending in stories, 1954. Intransitive sense "march in a line (as soldiers do) one after another" is from 1610s. Related: Filed; filing.

1841 in cookery, reborrowing from French of the same word that had been taken 14c. and Englished as fillet (q.v.). Filet mignon (literally "dainty fillet") for "small, round, tender cut of meat from the center of the fillet" 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]

*gwhī-, Proto-Indo-European root meaning "thread, tendon."

It forms all or part of: defile (n.) "narrow passage;" enfilade; filament; file (v.1) "place (papers) in consecutive order for future reference;" filigree; filipendulous; fillet; profile.

It is the hypothetical source of/evidence for its existence is provided by: Avestan jya- "bowstring;" Latin filum "a thread, string;" Armenian jil "sinew, string, line;" Lithuanian gysla "vein, sinew;" Old Church Slavonic zila "vein."