The tone of the debate that lasted nearly two hours in a Paris hotel was polite and calm but the struggle by both candidates to woo the 6.8 million voters who backed Bayrou in last week's first round of voting looks set to continue.
Bayrou said that he was in "profound disagreement" with the Socialist on her economic proposals which he argued relied too heavily on state intervention.
Royal will now go head-to-head with Sarkozy in a televised debate on Wednesday evening.
Royal described Saturday's unusual debate as "an unprecedented event that underscores the modernisation of politics and the need to break out of confrontation between blocs."
But during campaigning in the northern town of Valenciennes on Saturday, the same debate was dismissed by Sarkozy as "small-time scheming" and he declared it held little interest for him.
|Bayrou, right, said that he continued to |
disagree with Royal on economic policy [AFP]
The debate was initially to be shown on CanalPlus,
but the station cancelled it, citing electoral commission rules that both candidates should receive equal airtime.
A little known digital channel decided to air the debate instead.
Sarkozy, who was accompanied on the campaign trail by the French employment minister, said: "They are together in a grand Paris hotel, but I am here in Valenciennes with Jean-Louis Borloo on the ground."
Some observers said Royal had succeeded in showing that she was open to discussion with a politician who did not share all of her ideas, addressing a theme that was central to Bayrou's campaign - transcending the left-right divide.
But she has faced criticism within her Socialist party for the debate with Bayrou and engineering a shift to the centre that could imprint on the future direction of the Socialist party.
Sarkozy, the candidate of Jacques Chirac's governing UMP party, has refused to hold direct discussions with Bayrou but has welcomed 19 of the 29 elected deputies of his small Union for French Democracy (UDF) into his fold.
A new poll showed that 35 per cent of Bayrou's voters would back Royal in the runoff compared with 29 per cent for Sarkozy, while 36 per cent planned to abstain or had yet to make up their minds.
Sarkozy still remains the favoruite with 52.5 per cent of voter intentions against 47.5 per cent for Royal, according to the Ipsos/Dell survey.