Kinloch (Ancient Scottish Ballads, 89) printed a text in which the king (not imprisoned) is the king of France on a long hunting-trip. He speculated that "Willie" was James V of Scotland, who went in disguise to "inspect" the Duke of Vendôme's daughter as a marriage prospect. He decided against her, but then met the French princess at a hunting party. She was keen, but was too ill to travel and died six months after her marriage. (see Child, II, 399). Unlikely, really; and we don't know whether the song started out in Scotland or England anyway.

On the whole, looking for real events behind classic ballads (especially when the ballads are probably much more recent than their supposed historical inspirations) is a bit of a lost cause. Once in a while you can get somewhere, of course, but an awful lot of effort has gone into inconclusive speculation (sometimes frankly bizarre) over the years.