Sir Thomas Urquhart, who among many other accomplishments wrote a book with the title Logopandecteision, or, An Introduction to the Universal Language, wrote in a work of 1652 of “The Gasconads of France, Rodomontads of Spain, Fanfaronads of Italy.” He was well travelled and claimed to be fluent in the languages of all these countries, so he might equally have said the word was Spanish or French, though that would have spoiled his roll-call of countries.
English borrowed it directly from the French fanfaronnade with the same sense of arrogant or boastful talk. This derives from fanfaron, a braggart, which in its turn comes from fanfare, the same word as in English. So a person guilty of fanfaronade is blowing his own trumpet.
It’s far from being a compliment. As Sir Walter Scott narrated in The Surgeon’s Daughter, one of his Chronicles of the Canongate, dated 1827: “Dr Gray ... was an enemy to every thing that approached to fanfaronade, and knew enough of the world to lay it down as a sort of general rule, that he who talks a great deal of fighting is seldom a brave soldier, and he who always speaks about wealth is seldom a rich man at bottom.”
At about this time, the word returned to its roots and could mean a literal fanfare. Charles Dickens used it like that in one of his short stories, Somebody’s Luggage of 1862: “And hark! fanfaronade of trumpets, and here into the Great Place, resplendent in an open carriage, with four gorgeously-attired servitors up behind, playing horns, drums, and cymbals, rolled ‘the Daughter of a Physician’ in massive golden chains and ear-rings, and blue-feathered hat.”
You might prefer one or other of Urquhart’s alternatives, both also of European origin. A gasconade was also extravagant boasting, in reference to a supposed characteristic of the Gascons of SW France. See also rodomontade.