When a Green party activist was headbutted in the street, his attackers told him there was more to come when the far right's Jordan Bardella wins France's parliamentary election. A Muslim family received a note with similar threats.

Hours after Bardella's National Rally (RN) party scored big in the European election this month, four men in Paris assaulted a teenager at whom they hurled homophobic and transphobic slurs.

The four, who were found guilty and sentenced after the attack, told police they were RN party members and members of the violent far-right GUD group, the Paris prosecutor's office said.

While the interior ministry says it does not have consolidated numbers on such incidents, they offer a snapshot of what rights groups say are a rising number of assaults motivated by race, religion, homophobia, transphobia and political allegiance during campaigning for France's snap election.

The RN says it has no links to violent far-right and neo-Nazi groups. It did not reply to a request for comment about the spate of incidents since the European election.

Opinion polls project the RN will emerge as the dominant political power after the two rounds on Sunday and July 7, winning support from French people who say President Emmanuel Macron's centre-right party has ignored their concerns about the rising cost of living and weaker public services.

"We'll smash you, Bardella will win, and it starts now," Green party activist Olivier Richard recounted the two young attackers as saying. They headbutted him in the face in Bordeaux as he carried pamphlets for the left-wing New Popular Front, which is expected to come second in the vote.

"They were sure they were going to win and could do what they wanted. This situation is terrifying," Richard said.