Interesting question. It isn't French, exactly. Princess Chantal (daughter of Prince Henri, Comte de Paris - one of the pretenders to the French throne) is the origin of it in France; she named her daughter Kildine in 1979. She got it from the title of a book she'd had as a child, written by Queen Marie of Romania: 'Kildine, histoire d’une méchante petite princesse' (Kildine, story of a naughty little princess), published in the 1930s. The book is a fairy-tale, so I imagine that Queen Marie (one of Queen Victoria's grand-daughters, and born in England) made the name up.
It looks like it's also a really rare and possibly defunct Irish surname, so maybe that's where she got it from. But it seems more likely to me that she just invented it for the story.
This message was edited by the author on October 12, 2011 at 7:41:20 AM