This is a reproduction Kepi Hat from a ex BBC drama prop box and cost me £2
The Kepi hat is most commonly associated with the French army, french police or american civil war.
The badge, colours and style of this one as far is as I can tell make it a copy of a WWII French Foreign Legion Kepi Hat.
The term Kepi is french word which respelled from German word Kappe, which means Cap.