Name the pocketwatch music in "Time After Time"

I saw this movie over the weekend on one of my movie channels - hadn’t seen it in about ten years. I forgot how great that movie is - Sci Fi, lots of SF locales, Jack the Ripper, two of the all-time great Sci Fi actors… (although it was slightly more difficult to meet single SF women back when I was single, but I digress)…

Anyway, that friggin’ pocketwatch music that Jack the Ripper played before killing someone has been in my head for two days now. For the life of me, I cannot get rid of it. It’s killing me. I feel like I’m in that Vonnegut story and the Gov’t is piping this music into my head to keep me stupid. I want to beat the side of my head like Rainman.

Does anyone know what song that is? Does anyone recognize it from any other movie? IMDB didn’t exactly have a “soundtrack listing” for it…was it created for the movie?

Any…do do de doo do…help would be…doo de doo de doo de doo de…appreciated…

The best that I could find is that it is a French medieval melody.
http://www.geocities.com/baddi_101/time.html