An Australian magistrate has jailed a man for an abusive tirade against a French tourist on a Melbourne bus in which he told her to "speak English or die", reports said on Thursday.

The young woman, Fanny Desaintjores, was with friends on the bus and singing in French when David Graham launched the verbal attack in November 2012. A video of the incident soon went viral and has been watched almost 5 million times.

(Warning: the video contains abusive and racist language)

During his outburst, which was filmed by a passenger with a mobile phone, Graham said he would cut off Desaintjores' breasts and made insulting comments about her appearance.

Magistrate Jennifer Anne Benn Goldsbrough said the comments were "overwhelmingly sexist, misogynist remarks and occasionally racist", The Age newspaper reported online.

"It was not a horrible, offensive throwaway line but an ongoing tirade of vile, offensive, aggressive words," she said of the attack, which other passengers joined in on.

The magistrate jailed Graham, who pleaded guilty, for 21 days.

Desaintjores, who is in her early twenties, told Fairfax media back in 2012 that at first she had thought the abuse was a joke but later became afraid she
would be physically assaulted.

"I thought he was kind of joking at first and then I realised he wasn't kidding at all, so my friends and I stopped laughing," she said at the time. 

"We were quite afraid that he (would come) and hit us."

When another man, who had also taken part in the abuse, smashed a window near her as he got off the bus, Desaintjores said she became "really scared".

"I realise that maybe we shouldn't sing in a public transport, but I think that's insane that they reacted like that, we're all adults," she said.