In Nancy Toff's essential The Flute Book, she explains that the term flautist is associated with the negative connotations derived from the Latin verb, flaut which means to jeer or mock, which "apparently derives its meaning from the practice of playing a flute to ridicule."
According to the Oxford English Dictionary, the term flautist did not appear in English until 1860, when Nathaniel Hawthorne used it in The Marble Faun. ("The flautist poured his breath in quick puffs of jollity") The frequent use of the word flautist is probably inspired by the Italian terminology, flauto which pervades musical scores. Significantly, Hawthorne had lived in Italy for a yeard and a half before he wrote The Marble Faun.
The Oxford English Dictionary states that the word flutist (1603) is a much older established word than flautist (1860). Since the English term flute is related to the modern French flūte, it follows therefore that the player of that instrument would be a flutist.
Toff pleads calling her a flute player, or even fluter, a term coined by Saumuel Pepys. (His diary entry for June 21, 1666 notes, "I saw...a picture of a fluter playing on his flute.") Flutist, fluter, or flute-player...but please, not flautist!
Toff, Nancy. The Flute Book.
Oxford University Press, Inc. New York: 1996.