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

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 on June 17.

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

“It’s a good result tonight ... but we have to remain mobilised for the second round,” said Foreign Minister Laurent Fabius.

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 per cent and 35 per cent of the nationwide vote, while UMP candidates and their allies won between 34 per cent and 35 per cent.

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

Ms. Le Pen said she came in first in the northern district where she is seeking a seat, but faces a run-off against a Socialist candidate.

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

Mr. Sarkozy’s former Prime Minister, Francois Fillon, warned that Mr. 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 Mr. Hollande’s election, Mr. Fillon said after Sunday’s results started coming in.

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