French citizens from some overseas regions have begun voting in the country's presidential election.
Sarkozy and Royal had an acrimonious exchange on Friday
The first votes were cast in Saint Pierre and Miquelon off eastern Canada - but voting in mainland France will be on Sunday.
Socialist Segolene Royal is battling conservative candidate Nicolas Sarkozy.
In the final day of campaigning on Friday, Ms Royal said her rival's election might spark riots. Mr Sarkozy accused her of verbal violence.
Voting got under way on Saturday in the tiny French territory of Saint Pierre and Miquelon, which has 5,000 registered voters in a population of 6,300.
Voting also takes place early in French Guyana and the Caribbean islands of Martinique and Guadeloupe to offset problems of time difference.
Mainland polling booths open at 0800 (0600 GMT) on Sunday.
On the last day of campaigning on Friday Ms Royal said that electing Mr Sarkozy could spark riots and violence and that he was a "dangerous choice".
"It is my responsibility today to alert people to the risk of [his] candidature with regards to the violence and brutality that would be unleashed in the country," she said.
Mr Sarkozy reacted angrily, accusing Ms Royal of breaking "elementary rules of democracy".
He said he could not understand why Ms Royal had felt the need to resort to "verbal violence".
"I told Ms Royal that politics should be about respect, openness, tolerance, unity. I feel she's just ending with violence, a certain feverishness. France deserves something else."
Ms Royal, a former environment minister who hopes to become the first woman president of France, has made her opponent's divisive character the centre of her campaign, says the BBC's Oana Lungescu, in Paris.
Centrist Francois Bayrou, defeated in the first round of voting, has said he will not vote for Mr Sarkozy.
The remaining rivals held one, sometimes ill-tempered, TV debate on Wednesday, watched by an estimated 23m people, that left both claiming victory.
But Ms Royal was the one who seemed to lose her cool during the debate, while Mr Sarkozy appeared increasingly presidential, our correspondent says.
France is electing a successor to Jacques Chirac, 74, who has been president since 1995.