The election also spells trouble for the far-right National Front (FN), which is expected to win only one to six seats, when it had hoped to secure a "massive" presence in parliament.
The polls, by Kantar-Sofres and Ipsos/Sopra Steria, projected the main opposition force would be conservative party The Republicans and its allies with between 125 and 133 seats.
The novice La Republique En Marche party and its political ally - the Mouvement Démocrate (MoDem) - won a combined 32.3% of the vote in the election's first round.
The Associated Press on Sunday reported that Macron's party had 41 percent of the vote after 57 percent of the vote had been counted.
"One year ago no one would have imagined such a political renewal", Prime Minister Edouard Philippe said in a statement.
A total of 573 of 577 seats in the French Lower House will be contested in the second round, after four were settled in the first round last week.
One target this week was Olivia Gregoire who is standing for a seat from a constituency in wealthy southwest Paris and whose posters, like most REM candidates, feature Macron's face prominently. (LREM) political movement is set Sunday to win a sweeping parliamentary majority in a run-off vote.
Turkish president slams US charges for guards
Mr Newsham said there was no probable cause to arrest Mr Erdogan, who watched the confrontation unfold from a nearby vehicle . Correction: June 15, 2016A previous version of this article misidentified the gender of one of the people charged today.
That's also much lower than the midday turnout in the first round of parliamentary elections on June 11, which was at 19.24 percent, according to FranceInfo. Overall, the first-round vote saw record low voter interest, with less than half of France's 47.5 million voters taking part overall.
That's the biggest victory in at least 15 years, though the vote also saw the lowest turnout ever for a French parliamentary election, a sign of the disenfranchisement and frustration that has characterized this year's campaigns.
Jack Lang, the President of the Paris Institut du Monde Arabe, French politician and former French Minister of Culture, was optimistic about relations between Morocco and France under Emmanuel Macron in a recent interview with the Maghreb Arabe Presse.
That would allow Macron to move fast with promised legislation, notably on changing labor laws to make hiring and firing easier.
Pollsters predict the party will lose well over 200 seats after its five years in power under former president Francois Hollande, leaving them with only around 20.
While French voters have handed past presidents large majorities in parliament, what's different this time is that Macron's party is splitting - and therefore weakening - the opposition.
The voting system punishes parties outside the mainstream, or with no mainstream allies, like Le Pen's National Front.