But while Macron's LRM party is pushing traditional parties into irrelevance, it is not getting a strong mandate from French voters.
To achieve that, a candidate would need more than half of the votes and that must account for at least a quarter of registered voters.
The conservative Republicans had 16 percent, followed by the far-right National Front with 14 percent. The party got just over 13 percent of the vote. But Macron's impressive performance in his first month, coupled with astute moves, including naming an LR deputy as prime minister, took the wind from their sails.
"If we really want him (Macron) to change things he needs a majority", 67-year-old voter Irena Plewa, a pensioner, said at a bustling Paris food market.
Melenchon, who could see his party win around 20 seats, asked French voters "not to give full powers" to the president's party in the second round next week.
Rivals began sounding the alarm regarding the majority, with Jean-Christophe Cambadelis, head of the Socialist Party, remarking that opposition almost no longer exists, and Marine Le Pen calling the abstention rate "catastrophic".
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The Cuban government has made clear it will not be pressured into political reforms in exchange for diplomatic engagement. And Americans can still self-certify under a general license that they are traveling to Cuba for legitimate reasons.
Kathleen Brooks, research director at City Index, said: "The euro is starting to look strong and stable: it has growth, subdued political risk, and a potential wavering European Central Bank on its side".
Centrist Emmanuel Macron was sworn in as the eighth president of the French Fifth Republic in a ceremony at the Elysee Palace on Sunday. "Next Sunday, the National Assembly will embody the new face of our republic".
Francois Baroin, the campaign leader for the Republicans party, noted that "the level of abstention ... demonstrates the persistence of divides in French society".
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.
On the right, the conservative Republicans were also reeling, projected to end up with possibly no more than 110 seats, and possibly as few as 70, having controlled 215 in the outgoing parliament.
She also slammed the electoral system as unfavorable to smaller parties like hers.
German Chancellor Angela Merkel congratulated the French President on Monday.
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La Republique en Marche (The Republic on the Move, LREM) and allies, with an estimated 32.9 per cent of the vote, is expected to take between 400 and 440 of the assembly's 577 seats in next week's second round, according to a Kantar Public-onepoint forecast based on partial results.
The far-right National Front party failed to capitalize on Marine Le Pen's record score of 33.9 percent of the presidential second round vote.
Socialist Party leader Jean-Christophe Cambadelis, who was eliminated in Paris, called the results "an unprecedented step back for the left as a whole and the PS (Socialist Party) in particular".
The Socialist Party - now the largest party in the National Assembly - scored the biggest loss of the night, taking just 9.5 per cent of the vote with its allies.
Mr Macron also plans to quickly pass a law to strengthen security measures - effectively making the state of emergency permanent and another one that he says will put more ethics into French politics.
Turnout this year was lower than in the past two legislative elections, 57 percent in 2012 and 60 percent in 2007.
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The suspect suffered a gunshot wound, but it was not immediately clear if he was hit by troopers or if it was self-inflicted. The suspect drove much of the pursuit on damaged tires after he struck stop sticks but did not stop, police said.
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