A famous bearer is the actress Fran Drescher (born Francine Joy Drescher on September 30, 1957.) She was the star of "The Nanny" and "Living With Fran."
In response to what CharlieRob and Surreal said, Francesca and Francine are variants of Frances in different languages, so of course the name could be short for those names. I believe that only Frances is listed because it is the English version of the name, and this site is written in the English language.