Melissa is an ancient Greek name that comes from melli, "honey". Like many classical names, it's used internationally with slight variations. The main difference in French is that you would usually write it with an acute accent over the letter "e" ("Mélissa").
If you watch http://www.youtube.com/watch?v=QWTNj8Vej5w, you will hear how the French DJ pronounces the name when he mentions Mélissa Theuriau just after 00:16.
