PARIS - Leftist candidates led the first round of France’s parliamentary elections Sunday, according to polling agencies and partial official results, 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, which is dominated by conservatives, to carry out his plans to redirect France’s economy, with repercussions around debt-laden Europe. Conservatives said the Socialists’ spending plans could cripple France just as it and other European countries are being asked to rescue Spain.

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. Socialists already control the Senate and lead most of France’s regions and its local governments.

Four polling agencies’ projections and early official results show diminished support for former president Nicolas Sarkozy’s conservative UMP party across the country. 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.

Socialists or other leftists were leading in 70 of 116 districts where the vote count was complete Sunday evening, according to official results.

The Interior Ministry is releasing results gradually through the night, district by district.

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 estimated that Socialists and other leftists won between 43 percent and 48 percent of the nationwide vote, while UMP candidates and their allies won between 34 percent and 35 percent.

The polling agency projections are based on actual vote results in select polling stations nationwide, and were largely in line with expectations. Turnout was relatively low, at 57 percent, well below the 63 percent in the last parliamentary elections five years ago.

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

However, the polling agencies predicted that the National Front 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 tough runoff against a Socialist.

Candidates who win support from more than 50 percent of registered voters win the seat outright. Most races go to a runoff, involving any candidate who garners more than 12.5 percent 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.

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.

Sarkozy’s campaign spokeswoman and a conservative parliamentary candidate, Nathalie Kosciusko-Morizet, claimed that Hollande’s team is already spending so much that it is taking France towards “bankruptcy, a Spain-like, Greek-like situation.’’

Hollande has pledged to cut debt but won election by arguing to voters that economic recovery does not have to be all about belt-tightening, as Germany has argued. Hollande says governments should invest in stimulus to grow.

Among Hollande’s first moves was to lower the minimum retirement age for some workers to 60, arguing that Sarkozy’s reform raising it to 62 had unfairly targeted the poorest workers. Hollande’s government also wants to create thousands of teaching jobs after education cuts under Sarkozy.

Voters casting ballots Sunday paid little attention to broader European concerns, focusing instead 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.’’

The new lower house serves for the next five years.