Opinion polls taken on the eve of the Sunday's first-round vote have consistently given Sarkozy a lead over Royal, putting Francois Bayrou, a centrist in third place and Jean-Marie Le Pen, the veteran far-right leader, in fourth.
But Bayrou and Le Pen will still be hopeful of securing a place in the run-off on May 6.
"Anything can happen!" the front-page headline of the Le Parisien
The Journal du Dimanche
declared: "Incredible suspense for an historic vote."Voting begins
About one million citizens in France's overseas territories and French residents in the Americas got voting under way on Saturday, in a move to encourage voter participation.
"It will be worrying times for France if Sarkozy wins the presidency"
Be Humble, UK
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Voting in mainland France began at 8am (06:00 GMT) on Sunday.
Around 44.5 million registered voters - an increase of 3.4 million on 2002 - were eligible to choose the successor to Jacques Chirac, who steps down next month after leading the country for 12 years.
Opinion polls giving an initial indication of the result are expected to be released straight after voting ends at 8pm (18:00 GMT).
Sarkozy, the son of a Hungarian immigrant, has pushed a programme based on the themes of work and national identity, but his proposed crackdowns on illegal immigration and crime have provoked fears he would divide rather than unite the nation.
The former interior minister smiled as he voted with his wife in the Neuilly-Sur-Seine suburb of Paris.
"What is very important is that the French come to vote in large numbers, that it is a great moment for French democracy," said.
Royal, an army officer's daughter, has presented herself as a nurturing mother figure and has proposed an economic programme that would keep France's generous welfare system intact.
"The French people know the importance of this vote, its seriousness, and I share their sentiment of living through a very important day," she said on Sunday.
Bayrou, a former Latin teacher, has said he wants to end the traditional left-right political divide by forming a national unity government.