PARIS — French President Francois Hollande’s Socialist Party won a solid majority in parliamentary elections Sunday, polling agencies projected, fortifying Hollande in his push for governments to spend money — not cut budgets — to tackle Europe’s economic crisis.
Former President Nicolas Sarkozy’s conservatives, who dominated the outgoing National Assembly, suffered a stinging loss, according to all estimations. Meanwhile, the far-right National Front party was on track to win a small but symbolically important presence in parliament for the first time in years.
‘‘This new, solid and large majority will allow us now to pass laws for change, and gives us great responsibilities in France and in Europe,’’ Foreign Minister Laurent Fabius said on France-2 television as the results started coming in.
Elections in France and Greece on Sunday will weigh on Europe’s future and whether its debt troubles will hobble markets and economies across the globe. France is the second-biggest economy in the eurozone and, along with powerhouse Germany, contributes heavily to bailouts for weaker nations and often drives EU-wide policy.
France’s Socialists will have between 308 and 320 seats in the 577-seat National Assembly after Sunday’s second-round parliamentary elections, the TNS-Sofres Sopra Group, Ipsos and CSA agencies estimated. The pollsters’ projections were based on actual vote counts in select districts around the nation.
That’s well over the 289 the Socialists needed for a majority, and it means they won’t have to rely on far-leftists who oppose some of Hollande’s pro-European policies to pass legislation.
It’s a stunning turnaround for the Socialists, a party that spent much of the last decade mired in division and confused about its direction. Hollande’s victory over Sarkozy on May 6 led the way for the leftists’ legislative sweep.
Hollande has said his first priorities for the new parliament include postponing a balanced budget until 2017, raising income taxes to 75 percent for those who earn more than €1 million ($1.26 million) a year, and hiring 60,000 new teachers. The Sarkozy government had imposed cuts on the education sector.
Under Sarkozy, France joined Germany in favoring government austerity measures instead of stimulus programs as the antidote to the continent’s debt troubles — especially in countries such as Greece that turned to the European Union and others for billions in bailout dollars.
A solid parliamentary majority for Hollande frees him up to make the changes to tax laws and impose the new spending he promised, and it gives him a stronger mandate to push for stimulus programs in global economic talks. He heads Monday to the G-20 summit in Mexico to meet leaders of the world’s most important economies.
Hollande’s push for government-sponsored stimulus programs has met opposition from German Chancellor Angela Merkel, but both have pledged to keep working together to ease Europe’s financial crisis.
Hollande presented other European leaders last week with a new ‘‘growth pact’’ that includes €120 billion ($151 billion) worth of spending measures around the continent to stimulate growth, French newspaper Journal du Dimanche reported Sunday. The paper said it obtained a copy of an 11-page letter on the issue sent to Merkel and others.
The new parliament will lean well left: the Socialists and allied parties, the Greens, and the Leftist Front parties are estimated to have 340 to 350 seats altogether.
Sarkozy’s UMP and its allies are estimated to get between 213 and 221 seats. UMP officials called for party unity after deep divisions during the election campaign over whether they should seek alliances with the far right, breaking down a moral barricade between mainstream conservatives from the anti-immigrant National Front party.
Party leader Marine Le Pen lost her own parliamentary race — by just 118 votes — but her niece and a prominent lawyer won seats for the party, which Le Pen called ‘‘an enormous success’’ after years outside parliament despite significant popular support.
In an embarrassment for the Socialists, former presidential candidate Segolene Royal lost her controversial campaign for a parliamentary seat, quashing her hopes of becoming speaker of the National Assembly.
Royal, a prominent Socialist, is Hollande’s ex-partner and the mother of his four children.
Her campaign became embroiled in controversy last week after Hollande’s current companion — journalist Valerie Trierweiler — expressed support for her opponent, dissident Socialist Olivier Falorni, on Twitter, seen by some as a show of jealousy.
The Socialist Party leadership had endorsed Royal, but Falorni refused to abandon the race in her favor.
Voter turnout was weak for France, at about 56 percent, as voters were asked to cast ballots for the fourth time in the past two months.
In a well-off area of central Paris, voter Eve Baume said she cast her ballot for the local Socialist, Claire Morel, ‘‘because I've been waiting for change for a long time. ... Also I wanted to support Francois Hollande, the government and its projects.’’
Pascal Albe, a voter from the working class Paris suburb of Ivry-sur-Seine, said that though he generally votes for the right, Hollande should have a Socialist-led parliament.
‘‘Otherwise the country will be paralyzed, and especially now, we don’t need that,’’ he said.
Cecile Brisson, Sylvie Corbet, Thibault Leroux and Catherine Gaschka in Paris contributed to this report.