Meanings
According to the Oxford English Dictionary, from the 18th-century custom among the French upper class of leaving receptions etc. without formally announcing each departure to the host or hostess. Compare Spanish irse a la francesa and Portuguese sair à francesa ("go in the French manner") but also the otherwise ubiquitous attribution of this behavior to the English as with French filer à l’anglaise ("leave in the English manner"), Italian filarsela all'inglese, Polish wyjść po angielsku, etc.
How to pronounce "French leave":
A departure taken suddenly, without announcement, and/or without permission.
Example: "to take a French leave"
Synonym of AWOL: absence from military service without permission, especially temporary shirking of duty subject to punishment.