Historically, falernum is ancient Roman. It used to be a wine made from grapes growing in vineyards on the flanks of Mount Falernus, half an hour south of Rome. Falernian wine in Latin = Falernum.
The Romans would make this wine from Aglianico grapes for example, and spice it with lemons, herbs, botanicals such as cinnamon, cloves and add a Sicilian invention: Orzata which evolved into orgeat. The wine was usually made and kept for special occasions such as weddings.
Praised by historical Roman figures such as Cicero and Crassus, just about all written documentation about falernum disappeared with the decline and downfall of the Roman Empire, only to resurface around the 18th century in Barbados and Jamaica.