The Fantasticks actually began life as a long worked on script called Joy Comes to Dead Horse a full blown musical in the Rodger's and Hammerstein style. Jones and Schmidt had worked on the script for years. They were challenged by director Word Baker to finish the script in 3 weeks with a promise of a performance in 3 weeks hence (more on that later).
The inspiration for the musical was Rostand's (of Cyrano de Bergerac fame) Les Romanesques. The more commonly used title was The Romancers. George Fleming, however, named her 1900 version The Fantasticks, literally translated a "romanesque" or one who is romantic.
Fleming added the extra "K" . It added a bit of whimsy and a sense of the plays spirit.
Harvey Scmidt was delighted by the discovery of this "new" title and as a graphic artist liked the way it looked. That extra tall letter near the end of the word "acted to frame the word squarely instead of letting it slope away."
So there it is; the birth of a title.