Furlough was imported in the 1620s Dutch word verlof (meaning permission) to mean a leave of absence from the military. Verlof is made up of two parts, the Middle Dutch ver- (completely, for) and laf (permission). Laf originally comes from Proto-Germanic *laubo.
In English the parts are for and leave. There is an alternate spelling furloe in the 18th century but furlough was the original modern form and the one still used today. The spelling is most likely to show pronunciation as it does not follow Dutch/Germanic spelling/pronunciation norms.
The word was first used as a verb in 1873 to mean granting leave of absence (to a soldier). It was used to mean lay off or suspend temporarily in reference to employees by the 1940s (originally of civilian employees in the US military).