The top two candidates in the first round of the French presidential election are beginning intense campaigning for the run-off on 6 May.
Ms Royal and Mr Sarkozy represent a break with old-style French politics
Centre-right candidate Nicolas Sarkozy and Socialist Segolene Royal defeated 10 others in Sunday's ballot, with a record voter turnout of nearly 85%.
Mr Sarkozy garnered 31% of the vote, while Ms Royal, bidding to be France's first female leader, took nearly 26%.
Opinion polls after the result showed Mr Sarkozy would win the run-off.
On Monday, Mr Sarkozy is due to address a rally in the eastern city of Dijon and Ms Royal is due in Valence, in southern France.
Voters are now faced with a clear left-right choice.
That political divide may be a return to French tradition, but both candidates are something new for France, says the BBC's Caroline Wyatt in Paris.
Mr Sarkozy, the son of a Hungarian immigrant, has a free market stance that sometimes seems closer to that of Britain or the US and an aggressive image that is also a departure from the patrician style of past presidents.
He is hated by the left as a reformer who many fear would change the French way of life by making the nation work harder and longer and by cutting back on its generous welfare state.
Ms Royal is a woman who fought her way to the candidacy against the will of her senior Socialist colleagues, our correspondent says.
Her campaign has been dogged by wrangles over policy and a series of gaffes.
She is a regional leader whose presidential pledges include a higher minimum wage along with a new form of youth job contract, to ensure that the young in France have a chance of entering the tough job market that all but the best-qualified feel excluded from.
But the run-off could be won by an appeal to the middle ground - and the 18% of voters who supported the centrist Francois Bayrou on Sunday, our correspondent says.
Mr Sarkozy addressed a cheering crowd at his election headquarters, after winning the highest number of votes for a candidate in the first round since 1974.
He said France had chosen to have a real debate between two different types of politics and asked people to rally behind him.
Ms Royal said she represented those who wanted to "reform France without brutalising it".
She is said to have already received pledges of support from the other six left-wing candidates who won a total of about 10%.
But the far-right National Front, whose leader Jean-Marie Le Pen failed to reach the second round as he did in 2002, said their voters "were not for sale" - an apparent warning shot to Mr Sarkozy.
Opinion polls taken after Sunday's results gave Mr Sarkozy between 52 and 54% of the vote - against 46 and 48% for Ms Royal.
And only 14% were uncertain of who they wanted to cast their ballot for.