OED
The Oxford English Dictionary defines far out as:
Of jazz: of the latest or most progressive kind. More generally, avant-garde, far-fetched; excellent, splendid. orig. U.S.
Their first quotation is an 8th November 1954 Time Magazine article entitled "Far-Out Words for Cats":
Jazz lingo becomes obsolescent almost as fast as it reaches the public ear.‥ A daring performance was ‘hot’, then ‘cool’, and now is ‘far out’.
1940s
We can see this term beginning to emerge in Simon Michael Bessie's 1938 book Jazz Journalism: The Story of the Tabloid Newspapers:
The third class, divertingly far out on the lunatic fringe, embraces such journalistic peep-shows as Bernarr Macfadden's New York Evening Graphic.
Whilst the book is about tabloid papers and not jazz, it shows "far out" being applied to something novel and possibly avant-garde.
Here's Esquire's 1946 Jazz Book applying it to jazz of the most progressive kind:
Much of its drive came from two other jazzmen on this list: drummer Davey Tough and bassist Chubby Jackson. Both are incomparable musicians; both have contributed mightily to that spark and zest which are so characteristic of Woody's band and which take it far out of the realm of the typical swing band.
Here's another snippet, from a 1947 The Jazz Record:
George [Lugg] sat staring miserably at the floor, and when the trombone solos came along he made impatient gestures and said: "That wasn't what I wanted to do at all." But in some of those ensemble passages, banging away behind Goodwin's trumpet and Scott's clarinet, with a good rhythm section pushing, he began to grin and nod his head. "That's it!" he'd say. 'That's good." He was so impersonal, so far out of himself, a musician listening to music and judging it by what he heard.
And from the next page:
Shuffle up that "Chain Gang" thing. Hear this cat blowing blue in the lost reaches of the world's last swamp. Go with this Yank into the eternal night, so far out of the world that nothing remains but the half-remembered crying of a horn. Born of slavery's misery comes jazz, bringing the gap from cat to cat with a blue bridge.
These may not be the exact use of the phrase, but give an indication of how it came around.
1954
It appears to have used as a set term in a publication of the South Dakota State University sometime in 1954:
... Ella Fitzgerald and hundreds of other "cats." To put expression for our word "darin;[?] into jazz terms, the jazz today is "far-out".
Billboard of 24 April 1954 reviews Les Elgart Orchestra's song "East is East":
A pretty instrumental with an exotic Oriental flavor. The virtuosity of Elgart's intrumentalists makes for easy listening, but there is a solid beat here for dancing. A little on the modern side, but not too far out.
Billboard of 26 June 1954 reviews Serena Shaw's "St. Louis Blues":
Here is the perennial as you might expect Yma Sumac to sing it. Miss Shaw, aided by exotic sounds from drums, organ and echo chamber, soars up and zooms down a two-octave range at a dizzying pace, working up to a frantic pitch at the end. It's pretty far out, but deejays might find it unusual programming.
The same November 8, 1954 Time Magazine cited by the OED had another article that used:
Says Jazz Promoter Norman Granz, who does not always understand [David] Brubeck's "far-out" music: "He's way out on Cloud 7."
From the 1811 Dictionary of the Vulgar Tongue.
FRENCHIFIED. Infected with the venereal disease.
The mort is Frenchified: the wench is infected.
And just a few lines above...
FRENCH DISEASE. The venereal disease, said to have been
imported from France. French gout; the same. He suffered
by a blow over the snout with a French faggot−stick;
i.e. he lost his nose by the pox.
I'd like to seize the opportunity to clarify the circumstances of the phrase French Disease.
The story of the French disease as far as I know it, is as follows (also confirmed in the Wikipedia article about syphilis).
From a previous life in Naples I remember being struck by the fact that syphilis which I knew was known in Medieval France as mal de Naples was symmetrically known in Naples as mal francese.
Around the same time I was reading the book "Love stories of French History" of which I can't resist citing (translating) the tastier (albeit heavily romanticised) relevant excerpts...
We are in April 1495 in Naples; America has been discovered 3 years ago and the French king Charles VIII has just sent the incumbent Spanish king of Naples Alfonso II away for a while. Charles gives splendid banquets to celebrate his new possession... (op. cit. p. 268).
One fine day, a knight started to feel a funny tingle. On the following day the itching turned into aches and his body was soon covered with poxes.
Understandably anxious he called for the doctor who actually could not come to help, for at the same time nearly all the king's guests were subject to the same mysterious illness.
The poor souls were paying a heavy price for a short lapse of entertainment; they were covered with blisters; some were loosing their lips or their eyes and those were the luckiest, for they were spared the painful sight of witnessing their "virility" dropping on the floor like a ripe fruit...
[...]
In actuality they had been contaminated by syphilis contracted by Christopher Columbus sailors and imported in Italy by the Spanish mercenaries serving the ousted Spanish King.
The disease spread like wildfire and even high ranking personalities were affected. Bishops and Cardinals lost their nose and even the Pope was not spared. Charitable doctors then eruditely revealed that the ailment could propagate in the air through breath and even in holy water, so that the honour of the holy men was safe.
As the king's army pathetically limped back northwards to France, wary Italians on the way kept aloof lest they would be contaminated by what thence came to be known as the mal francese - the French disease.
Best Answer
OED has it "of uncertain origin", although "individual-needs" is a possibility.