PARIS (AP) — French President Francois Hollande’s Socialist Party won a solid majority in parliamentary elections Sunday, polls projected, fortifying Hollande in his push for government stimulus programs 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.

The TNS-Sofres, Ipsos and CSA agencies estimate that the Socialists will have between 308 and 320 seats in the 577-seat National Assembly after Sunday’s second-round parliamentary elections. That’s well over the 289 they 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.

The new parliament will lean well left: the Socialists and allied parties, plus the left-leaning Greens, and the Leftist Front parties are estimated to have between 340 and 350 seats altogether.

Sarkozy’s UMP and its allies are estimated to have between 213 and 221 seats. Marine Le Pen’s anti-immigrant National Front party is projected to win one to four seats.

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 (euro) 1 million
($1.26 million) a year, and hiring 60,000 new teachers after education cuts under Sarkozy.

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 is Hollande’s
ex-partner and the mother of his four children. Her campaign became embroiled in controversy last week.