Is Cosette/Cozette even a name?
Upon reading the comments on Behindthename - not the most reliable, admittedly - I've learned that the background on Cosette is actually really murky.
Some say Hugo came up with it from the word chosette, which means "little thing." Cosette wasn't even her given name in the novel; it was Euphrasie and she was nicknamed Cosette by Fantine.
Others say it was derived from Colette, which is a variant on Nicole, hence where the nickname for Nicole origin came from.
The only thing I learned from reading this is that no one really knows :-) Oh, and that I should read the book. But, then - the book is always better and more interesting than a play or a movie!