Police have arrested two people in relation to a racist and sexist tirade on a French tourist aboard a Melbourne bus but say they are still looking for a man who instigated the verbal attack.

The pair, from Hampton Park, have been released without charge.

A police spokeswoman said a 24-year-old man and 21-year-old woman had been released pending further inquiries.

The French woman was called a c---, a dog and threatened with having her breasts cut off after she sang a song in her native language on the bus between Mordialloc and Caulfield on November 11.