Question: Origin of the French Curve, or mathematical definition

Everyone knows what a French curve is. Heck, some of us even have a set kicking around. But I have run into a brick wall in trying to find out how a french curve is actually made, or defined. Over several sessions, I can find nothing on the net that even hints at the answer.

French curves have been in use for ages, and they must have an origin. Either they are generated using some kind of function, or they were perhaps created in some freeform way and merely duplicated for generations, but there must be a precise answer. I remain perplexed that many math websites can have a page on the French Curve with a diagram and a line or two, and not tell how it was created, or how one would go about creating one.

Any answer or insight would be greatly appreciated. My apologies if this is not in the right forum.