Supporters of the Socialist Party candidate Francois Hollande gather outside the party headquarters ahead of initial results in French presidential elections in Paris, France on May 6, 2012.
Estimates from the French presidential run-off election show that the Socialist candidate Francois Hollande has won with 52 percent of the vote, ousting incumbent Nicolas Sarkozy.
Three polling institutes -- CSA, TNS Sofres and Ipsos -- estimated that Hollande had won 52 percent of the vote to Sarkozy's 48, based on samples of actual ballots taken from the Sunday polling.
Hollande supporters are gathering in his hometown of Tulle and in front of the Socialist Party headquarters in Paris, as rumors of the result spread across the country.
About 46 million people are eligible for voting in France. Polling stations in municipal buildings around the country opened from 8 a.m. to 6 p.m. (0600-1600GMT). In Paris and other large urban areas polls remained open until 8 p.m. (1800 GMT).
Hollande came first in the first round of the vote on April 22 with 28.63 percent of the votes, while Sarkozy garnered 27.18 percent.
Earlier, the candidates traded insults in a televised head-to-head debate.
Sarkozy labeled Hollande a liar and a "little slanderer" while Hollande accused Sarkozy of shirking his responsibilities, cronyism and favoring the privileged over France's poor.
Economy, unemployment and immigration policies are among the top issues considered by the voters.