PARIS — Leftist candidates won strong support in the first round of France's parliamentary elections Sunday, according to polling agencies, in a vote that is crucial to President Francois Hollande's Socialist agenda.

Hollande needs leftists to take control of the lower house of parliament — currently dominated by conservatives — to carry out his plans to redirect France's economy, with repercussions around debt-laden Europe.

Based on Sunday's first round, polling agencies predict that Socialists and other leftists will take a majority of the 577 seats in the National Assembly in the decisive second round June 17.

Four polling agencies' projections and early official results show diminished support for former President Nicolas Sarkozy's conservative UMP party. They show growing support for the left, amid anger at cost-cutting austerity measures and reforms under Sarkozy seen by some as too friendly to the rich.

"It's a good result tonight ... but we have to remain mobilized for the second round," said Foreign Minister Laurent Fabius, an influential Socialist.

The CSA and TNS-Sofres polling agencies predicted that leftists would take between 300 and 366 seats in the next parliament, and the conservatives between 210 and 270 seats.

Polling agencies CSA, TNS-Sofres, Ipsos and Ifop estimate that Socialists and their allies won between 31 percent and 35 percent of the nationwide vote, while UMP candidates and their allies won between 34 percent and 35 percent.

Other leftist parties expected to back Hollande — the communist-inspired Left Front and the environmental party The Greens — won another 12 percent to 13 percent of the vote, the polling agencies estimated.

The polling agency projections are based on actual vote results in select polling stations nationwide, and were largely in line with expectations. Official results were coming in district-by-district Sunday night.

Candidates of Marine Le Pen's far-right National Front party were projected to win between 13 percent and 14 percent of the vote in the first round.

However, the polling agencies predicted that the National Front, despite the relatively high voter support, would only get up to three members of parliament. That's because of a stigma against a party whose founder —Marine's father Jean-Marie Le Pen — has been convicted of racism and anti-Semitism.

Marine Le Pen said she came in first in the northern district where she is seeking a seat, but faces a runoff against a Socialist candidate.

Candidates who win more than 50 percent in the first round win the seat outright. Many races go to a second round, involving any candidate who garners more than 12.5 percent of the registered voters in the first round.

The result will affect whether Hollande can push his tax-the-rich, down-with-austerity agenda, and how much of a voice the far right will have in policies on immigration and Muslim practices.

Sarkozy's former prime minister, Francois Fillon, warned that Hollande might not get the powerful mandate he needs.

"There is a lot of concern about the first measures that were put in place" after Hollande's election, Fillon said after Sunday's results started coming in.

Among Hollande's first moves was to lower the minimum retirement age for some workers to 60, after Sarkozy and Fillon had raised it to 62. Hollande's government also wants to create thousands of teaching jobs after education cuts under Sarkozy.

Some voters are worried about handing so much power to the left, which generally favors higher government spending, at a time when Europe is struggling with huge debts that have forced Greece, Ireland, Portugal and now Spain to seek international financial help.

Socialists already have France's presidency, control the Senate, and lead most of France's regions and its local governments.

The National Front, buoyed by Marine Le Pen's strong third-place showing in the spring presidential race, is looking to build a presence in parliament for the first time since the 1980s. Her aims of undoing the euro currency, shrinking immigration, protecting "Frenchness" and fighting what she calls Islamization have won her fans around Europe.

The new lower house serves for the next five years, coinciding with Hollande's five-year term.

The results of France's parliamentary elections could have repercussions beyond its borders, notably Hollande's push against German-championed austerity measures for indebted European governments. But voters casting ballots Sunday were focusing more on local issues.

Paris voter Liliane Richard said she was voting for "my own ideas that I'm defending for daily life, for the youth. ... It's also very much about what's happening outside."

Most of Hollande's Cabinet members - 25 of 34 - are running for parliament seats as well, and they could lose their jobs if they don't win election.

Cecile Brisson, Elaine Ganley and Jeffrey Schaeffer in Paris contributed to this report.