The French woman targeted in a racist attack on a Melbourne bus earlier this month says she and her friends were terrified they would be physically assaulted by a group of fellow passengers.

It comes as police confirm they are investigating the tirade unleashed on Fanny Desaintjores aboard a bus travelling between Mordialloc and Caulfield, in which she was called a c---, a dog and threatened with having her breasts cut off after she sang a song in her native tongue.

Ms Desaintjores told Fairfax Media she and about nine friends were on the bus, having spent the day at the beach for a barbecue and enjoying the weather.