The Madame de Pompadour's birth name was Jeanne Antoinette Poisson, and although they weren't contemporaries (she died about twenty years before he was born), I was just wondering if there was any known connections between the two.
Though they share the same surname, I've never seen any connection mentioned between the two (except in this very questionable book and the author doesn't quote a source. It's very likely, judging by the quality of the study alltogether, that he just jumps to the conclusion because of the surname.)
You should also bare in mind, even though François Poisson was the official father of Jeanne (later to be Madame Pompadour), it is very likely that her real father was one of the many lovers of her mother.