A survey Thursday showed the conservative Sarkozy in the lead over the Socialist Royal with just three days to go until the election.
The debate drew more than 20 million viewers, showing how impassioned France's 44.5 million registered voters are about this election, with candidates offering strikingly different visions for the country's future.
Sarkozy, the more pro-market candidate, has been ahead in polls for months. Wednesday's prime time TV debate was Socialist Royal's last big chance to win over the centrist voters on whom the election hinges, seeking to convince them that her recipe for France's problems — more state aid and social protections — is the right course.
Royal went on the offensive, criticizing Sarkozy's record as former interior minister, repeatedly interrupting him and revealing a rarely-seen side of a candidate known for smiles and optimism.
She got furious when he started talking about handicapped children, saying he was "playing" with the issue. "I am very angry," said Royal.
Sarkozy grew testy: "Calm down, don't point at me with your finger like that."
"No, I won't calm down, I won't calm down," Royal said.
"To be president you have to be calm," said Sarkozy.
"Not when there is injustice. There is anger that is perfectly healthy because it relates to the suffering of people."
"Will you let me speak?"
"Even when I'm president of the Republic …" Royal said.
"That will be a happy thing," deadpanned Sarkozy.
"Because I know the effort that families and schools go through in order to welcome these children who no longer are welcomed. On this point I won't let the immorality of politics take over."
"I don't know why Madame Royal, who is usually calm, has lost her cool," said Sarkozy.
"I have not lost my cool, I'm angry. It's not the same, don't be contemptuous, Mr. Sarkozy, don't be contemptuous. I have not lost my cool, I'm angry. There is anger that is perfectly healthy and very useful."
"I wonder what it's like when you do lose your cool," said Sarkozy.
"I never lose my cool," Royal said. "I have a lot of cool."
"Well, if you say so, but you just lost it."
A former interior minister, Sarkozy said on Thursday he thought the debate was dignified, though he found Royal somewhat combative.
"I was a bit astonished at times by a certain aggressiveness in Madame Royal," he said in an interview on France's RTL radio.
"It can happen to anybody to lose their cool. Let's not be cross with her. It was no doubt the stress," he added.