To win, a candidate needs more than half of the votes cast, and they must account for at least a quarter of the registered voters - doubly challenging as the national turnout was below 50 per cent.
Her defeat in May brought huge relief to European allies who had feared another populist upheaval to follow Britain's Brexit vote and Donald Trump's election as US president, and disappointment to the party faithful.
French lawmakers are elected in two rounds.
The party's chief Jean-Christophe Cambadelis and its failed presidential candidate Benoit Hamon both lost their seats.
The Socialist Party that held power in the last legislature and its allies were all but vaporized - their 314 seats likely reduced, according to pollsters' projections, to as few as 20 seats, and possibly no more than 30, in the new assembly.
Far-left leader Jean-Luc Melenchon, who came in a strong fourth place in the presidential vote with almost 20 percent support, is running for a parliamentary seat in the southern city of Marseille.
Ms Le Pen's party took a disappointing 13.2 per cent, well below her 21.3 per cent of the presidential first round vote. The Socialists, party of former president François Hollande, didn't even make 10 percent.
Centrist Emmanuel Macron was sworn in as the eighth president of the French Fifth Republic in a ceremony at the Elysee Palace here on Sunday.
Blackhawks deal Panarin and Hjalmarsson, get Saad back
Combined with the Niklas Hjalmarsson deal , it seems the Blackhawks are shedding short-term deals for long-term ones. Hjalmarsson gives Arizona more stability on the back end after it traded away No. 1 goalie Mike Smith last weekend.
According to the French Interior Ministry, Macron's La Republique En Marche! movement - in alliance with the centrist MoDem party - gained 32.32 percent of the vote.
Jean-Luc Melenchon, a far-left candidate who also scored well in the presidentials, said Macron had won a "circumstantial majority".
The results, if confirmed, are another blow to the country's mainstream Socialist and conservative parties already reeling from Macron's election in May, which blew apart the left-right divide that has shaped French politics for the past century.
The lower turnout was mainly attributed to two major reasons - too intensive election arrangements, and the public's doubt over the French-style democracy and its effectiveness.
Francois Baroin, who led the campaign of the conservative Republicans, projected to win 80-100 seats, echoed the sentiment.
Despite the poor performance, Le Pen's control over the party remained too strong for any challenge to her leadership in the near future, he said, especially after her niece Marion Marechal-Le Pen stepped away from politics. If there is no clear victor, all candidates who win more than 12.5 percent in the first round qualify for a runoff.
Ifop pollster Frederic Dabi said a virtual monopoly on power would up the ante for Macron.
Meanwhile, Ms Le Pen came out on top in her constituency but appeared unlikely to turn her second place in the presidential contest into anything more than a handful of seats in Parliament. In a bid to renew the political scene, many have never stood for office before, such as Marie Sara, a rare female bullfighter, who is taking on a senior member of Le Pen's National Front in southern France, Gilbert Collard.
On the diplomatic front, Macron did not lose to U.S. President Donald Trump when they postured to shake hands together at the North Atlantic Treaty Organisation summit held in Brussels late May.