Was there a black market circa 1400s?
I would imagine so. At the very least, there would be merchants who dodge customs purely for tax reasons (more of a grey market, according to Wikipedia.) In the "illegal goods" sense, you'd probably see wartime societies impose rationing on food, iron, horses, and associated black market folks who supply those things to people and organizations who want them anyway.
Note that I speak with no weight of personal knowledge, merely a quick glance at Wikipedia and general understanding of human nature.
Yes this seems quite reasonable. I'm trudging through a Hundred Years War history right now, and there doesn't seem to have been the legal concept of "illegal goods" in the way that we understand it today. Aside from being practically unenforceable (and thus a waste of time) there wasn't much that would be considered bad (weapons were a necessity to travel it seems).
The closest would probably have been government control of certain goods, like wool in England. In certain circumstances they would enforce export bans to leverage the Flemish (and they hoped to drive up the price to pay off debt). One can imagine that clandestine smuggling would be in high order at those time. The dorf nobles already do this, though it is rather whimsical. 
If they did it to hurt the importer, that would setup a black market demand nicely.
When you have a highly centralized bureaucratic government like imperial China, on the other hand, you have both the ability to profit from strong government control of resources and strong incentives to ignore them and engage in black market activity.
Case is 11th century China, where the government controlled the salt trade for massive profits, but there was massive illegal production and sale. In a fragmented Europe before centralized states you might not see these as often as you might in Asia, with its powerful despotic governments.
