Fantastic Moon is one of two winners out of Frangipani (Jukebox Jury), who won at two in Germany, and a half-brother to a winner by Starspangledbanner. Frangipani is a half-sister to Fearless Hunter (Alhaarth), winner of the Gr.3 Marit Sveaas Minnelop.

Second dam Firedance (Lomitas) was a winner and has produced seven other winners, most notably Fearless Hunter and Fil Rouge (Lord Of England), Listed-placed in Scandinavia. She is a half-sister to the German Listed winner and sire Fabriano (Shardari) and to Germane (Distant Relative), winner of the Rockfel Stakes, then a Group 3.

Third dam Fraulein Tobin (J. O. Tobin) was a winner and is the grandam of Four Sins (Sinndar), a Group 2 winner in Ireland. She is a half-sister to the sire Running Stag (Cozzene), a multiple Grade 2 winner in the US who was Group 1-placed, and to two by Irish River: the Group 1-placed sire Blackwater, a Listed winner in France, and Bergenia, a Listed winner in Scandinavia.

This is the family of Lucky Chappy (High Chaparral), a Listed winner in Italy and third in the Grade 1 Hollywood Derby, out of Germane, who is also the grandam of the Listed winners Rewarded, Perfect Star and Connect and the ancestress of Kilmah (Sepoy), winner of the Gr.3 Prestige Stakes. The fourth dam Fruhlingstag (Orsini) was second in the Gr.1 Poule d'Essai des Pouliches, and her descendants include the Grade 1-winning sires Jack Christopher (Munnings), winner of the Grade 1 Champagne Stakes, and Street Boss (Street Cry).

Frangipani has an unraced two-year-old filly by Masar named Fire And Ice and a colt foal by Sea The Stars.