By 5:00pm (1500 GMT), turnout was 75.11 per cent against 73.87 per cent at the same time in the first round vote on April 22, the interior ministry said.
"It will be worrying times for France if Sarkozy wins the presidency"
Be Humble, UK
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Opinion polls giving an initial indication of the result were expected immediately after voting ends at 8:00 p.m. (1800 GMT).
First partial official results were due soon afterwards.
At a polling station near Paris' Champs-Elysees, Anne Combemale said she voted for Sarkozy because of his market-oriented economic platform.
Combemale, 43, who is unemployed, said: "He has the willpower to change France."
Bechir Chakroun, a 26-year-old who works in marketing, said he liked Royal's commitment to helping the poor.
"She represents change, I want to see what a woman can do."
Whoever wins the race to occupy the presidential palace, the Elysee, will mark a new political era in France as Jacques Chirac, 74, bows out after 12 years.
Sunday's vote marks the end of what has become an increasingly bitter race.
Sarko vs Sego
Sarkozy: Would abolish 35-hour week and exempt overtime from tax and social security. Retirement age of 60 to be viewed as minimum rather than maximum.
Royal: Would raise minimum wage and state pension. Unemployed would receive 90% of their salary for the first year of unemployment.
Sarkozy: Would create a ministry of immigration and national identity and endorse immigration favouring qualified workers. Minimum sentences for repeat offenders.
Royal: Would initiate bootcamps for young offenders.
Sarkozy: Would say EU negotiations with Turkey should result in strategic partnership not full membership.
Royal: Would put a
renegotiated EU treaty to a national referendum.
Shortly before campaigning officially ended on Friday night, Royal told RTL radio "choosing Nicolas Sarkozy would be 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 [if he won]," she said.
Pressed on whether there would actually be violence, Royal said: "I think so, I think so," referring specifically to France's volatile suburbs hit by widespread rioting in 2005.
A seemingly relaxed Sarkozy laughed off Royal's comments.
"She's not in a good mood this morning. It must be the opinion polls," he told Europe 1 radio.
"She's finishing in violence, in a certain state of feverishness," he later told reporters during a trip to the Alps.
Sarkozy topped the first round vote on April 22 with 31.2 per cent of the ballot against 25.9 per cent for Royal.
A key factor in Sunday's voting will be how the seven million people who backed the third placed centrist candidate, Francois Bayrou, in the first round vote in the second round.
Bayrou has not given his explicit support to either candidate but did say he would not vote for Sarkozy.
A TNS Sofres survey published on Friday showed Sarkozy at 54.5 per cent, compared to 45.5 per cent for Royal.
The last polls of the campaign, one by BVA and one by IPSOS, both put Sarkozy even further ahead on 55 per cent to Royal's 45.