French Socialists on course to score absolute majority in parliament French minister Cecile Duflot of the Greens votes in Sunday's election. The Greens are electoral allies of the Socialists. Photograph: Francois Guillot/AFP/Getty Images The left has scored well in the first round of French parliamentary elections, leaving the Socialist party within reach of an absolute majority that would give François Hollande, the president, a free hand in his approach to dealing with the economic crisis. The Socialists need 289 out of the 577 seats in the national assembly to take an absolute majority in the final runoff on Sunday 17 June. This would ensure Hollande has backing for his delicate balancing act of cutting the deficit while attempting to boost growth. First-round results show the Socialists are predicted to take between 275 and 315 seats, according to polling company TNS Sofres, and could make up the numbers with the backing of their electoral allies, the Greens. This means Hollande is less likely to be forced to chase the support of the hardline leftist Front de Gauche and Communists, who oppose him on certain key issues such as deficit cuts and the minimum wage, and which would have made for a tricky alliance. But although a Socialist absolute majority remains a possibility, it is far from a certainty. Socialist candidates are preparing for a tough fight in the final week of campaigning to bring voters out to the ballot boxes, after a record low first round turnout of 57%. The first round vote results suggest that the broad left will dominate parliament. Early results and estimates showed the left in general taking 47%, the right 35% and the far-right Front National 13%. The Front National, fresh from its high presidential election score in April, emerged as the third party in France in terms of vote-share. The Front National could now take two seats in the assembly - which would be the first time the party has sat in parliament in 25 years. One of the biggest defeats of Sunday evening was Jean-Luc Mélenchon, the firebrand hardline leftist from the Front de Gauche. He had stood in a high-profile, deprived Pas-de-Calais constituency in a personal battle against Front National leader Marine Le Pen, but was knocked out in the first round. Le Pen will now face a Socialist in the runoff. Mélenchon said he was disturbed by Le Pen's high score and would continue to fight the far right. If the Socialists win an absolute majority, it would be the first time in modern history that the party had control of both houses of the French parliament: the assembly and the senate.