(Ahem) Consanquinity.
I've been waiting for someone to start point to the various French royal family "batard", but they haven't.
Actually, a lot of those guys were off in other lines that didn't stand in line for the throne for any number of reasons. Until the formal establishment of the Royal Mistress (with a formerly Protestant King), the main line folks look to have been pretty well supervised by the various ladies in waiting, gentlemen of the guard, and so forth who actually watched everything these people did all their lives.
The King of France, sad to say, was watched in his toilet. I cannot imagine living a live with no privacy at all.