French socialist Francois Hollande has won a clear victory in the country's presidential election.Mr Hollande – who got an estimated 52% of votes in Sunday's run-off  -- said the French had chosen "change".Admitting defeat, centre-right incumbent Nicolas Sarkozy wished "good luck" to Mr Hollande.Analysts say the vote has wide implications for the whole eurozone. Mr Hollande has vowed to rework a deal on government debt in member countries.Shortly after polls closed at 20:00 (18:00 GMT), French media published projections based on partial results giving Mr Hollande a lead of almost four points. Turnout was about 80%.Exuberant Hollande supporters gathered on Place de la Bastille in Paris - a traditional rallying point of the Left - to celebrate.Mr Hollande - the first socialist to win the French presidency since Francois Mitterrand in the 1980s - gave his victory speech in his stronghold of Tulle in central France.He said he was "proud to have been capable of giving people hope again".He said he would push ahead with his pledge to refocus EU fiscal efforts from austerity to "growth"."Europe is watching us, austerity can no longer be the only option," he said.Mr Hollande has called for a renegotiation of a hard-won European treaty on budget discipline championed by German Chancellor Angela Merkel and Mr Sarkozy.However German Foreign Minister Guido Westerwelle welcomed the result, saying the two countries would work together on the debt crisis.UK Prime Minister David Cameron called Mr Hollande to congratulate him.Renewed relationsBut Mr the French election was closely followed way beyond Europe.In Rwanda, a country which has had a difficult past with France over the latter’s alleged role in the events that led up to the 1994 Genocide against the Tutsi, the Minister of Foreign Affairs, Louise Mushikiwabo told The New Times, last evening, "Rwanda respects the choice of the French people, and we look forward to furthering the renewed relations.”In an interview with Jeune Afrique last month, President Paul Kagame said he was open to working with whoever the French people would elect."I don’t know Francois Hollande but I remain open to pursue dialogue with the head of state chosen by the French people – whoever that will be,” said Mr Kagame.Last year, Kagame became the first post-Genocide Rwandan leader to pay a state visit to Paris, in what was viewed as a reciprocal gesture following the visit to Kigali by the now-outgoing French president Sarkozy in 2010.Under Sarkozy, France appeared keen on improving relations with Rwanda, which, in 2006, broke off diplomatic ties with Paris, over actions Kigali deemed were designed to rewrite the history of the Genocide against the Tutsi. Both countries have reopened embassies.But France remains home to several indicted Genocide fugitives.'Respect'In France, Mr Hollande capitalised on the country’s economic woes and President Sarkozy's unpopularity at home.The socialist candidate has promised to raise taxes on big corporations and people earning more than 1m euros a year.He wants to raise the minimum wage, hire 60,000 more teachers and lower the retirement age from 62 to 60 for some workers.In his concession speech, Mr Sarkozy told supporters: "Francois Hollande is the president of France and he must be respected."The outgoing president said he was "taking responsibility for defeat".Hinting about his future, he said: "My place will no longer be the same. My involvement in the life of my country will now be different."During the campaign, he had said he would leave politics if he lost the election.Mr Sarkozy, who stood on the Union pour un Mouvement Populaire ticket, has been in office since 2007. He had promised to reduce France's large budget deficit through spending cuts.He is the latest European leader to be voted out of office amid widespread voter anger at austerity measures triggered by the eurozone debt crisis.In Greece's parliamentary election on Sunday, voters turned against the two main parties which supported tough budget cuts.It is only the second time that an incumbent French president has failed to win re-election since the start of the Fifth Republic in 1958.The last was Valery Giscard d'Estaing, who lost to Mr Mitterrand in 1981.Mr Hollande is expected to be inaugurated later this month.A parliamentary election is due in June.