Police Thursday were investigating a torrent of threatening and racist abuse against a French woman on a Melbourne bus that was caught on camera and went viral on YouTube.

The woman and a group of friends were returning from a day at the beach when one of them began singing in her native tongue, which promoted an angry reaction from some passengers on the packed bus.

One aggressively demanded she “speak English or die” and then threatened to cut her breasts off.

Another man pushing a pram joined in, shouting that he would knife her.

The woman was then told: “Everybody on the bus wants to kill you” before the incident ended with a bus window being smashed.

The woman targeted, Fanny Desaintjores, told The Age newspaper she and her friends were terrified they would be physically assaulted.