I recognized it right away from having lived in France. Gillian Hills is/was -- in the tradition of Jane Birkin -- a talentless Brit who became famous in France.
Here's the song -- can't blame Don for being mortified (the video, at least, has a rather cute ending). And frankly, I am getting tired of Megan being passed off as "French," or as someone who "speaks French," when, in fact, she speaks Quebecois, which is a different (and far less attractive) thing.