Police have arrested two people over the racist and sexist tirade against a French woman on board a Melbourne bus.

A 24-year-old man and a 21-year-old woman, from Hampton Park, were detained early today and released pending further inquiries.

A video shows passengers verbally abusing Fanny Desaintjores, 22, and her friends on board a bus in the city's southern suburbs.

The footage, captured by stand-up comedian Mike Nayna, has been viewed more than a million times on YouTube and been reported around the world.

Mr Nayna said that after the Frenchwoman started singing in French, a female passenger chanted at her "Aussie, Aussie, Aussie", before another person shouted at her to "speak English or die".

Ms Desaintjores says she doesn't judge Australians for the isolated incident and she had never before experienced such hatred during a three-month trip through Australia.