Marine Le Pen, leader of the far-right Front National, was invited by television channel France 2 to debate Jean-Luc Mélenchon, the leader of the far-left Front de Gauche party.
The debate moderator, David Pujadas, tried to encourage Le Pen to respond to Mélenchon but she refused, even reading a newspaper at one point.
"This debate has no point," she said. "You don't have the same level of support as me."
Le Pen said she would prefer to be debating one of the two leading candidates, Nicolas Sarkozy or François Hollande, as she had a chance of meeting them in the second round of the election.
Le Pen also rounded on the TV channel which organised the debate, accusing it of only having viewing figures in mind.
"You might as well give us some boxing gloves," she said.
Mélenchon became increasingly irritated with his opponent, saying "looking at me when I speak to you" at one point.
Marine Le Pen is currently scoring between 15 and 20 percent in opinion polls, while Jean-Luc Mélenchon is attracting between 7 and 9 percent.
Despite the bizarre nature of the encounter, the programme attracted over 5 million viewers.