The result, if confirmed, redraws France's political landscape, humiliating the traditional Socialist and conservative parties that alternated in power for decades until Macron's election in May blew apart the left-right divide.
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.
The second round of the parliamentary election in France is slated for June 18, however, residents of Guadeloupe, French Guiana, Martinique, French Polynesia, Saint Barthelemy, Saint Martin, Saint Pierre and Miquelon can vote today.
French president Emmanuel Macron is holding a series of meetings with European leaders in Paris, as Brexit negotiations are due to start next week.
"We are the only force of resistance to the dilution of France, its social model and identity", Le Pen said in a televised address in her northern fiefdom of Henin-Beaumont.
Pollsters predict that Macron's La République En Marche (La REM) party will win as many as 75-80% of parliamentary seats in the Sunday elections.
French voters were expected to hand his year-old Republic on the Move party an overwhelming majority.
The victory of LRM, a political movement that was founded only a year ago and is still not officially organised as a party, will follow Macron's own victory with 66.1 percent against Le Pen in his first ever political campaign.
Ed Sheeran to receive an MBE from Queen Elizabeth II
Judy Murray and Heather Stanning are among the leading sporting figures to feature in the Queen's Birthday Honours list. The Pewsey man was also honoured for his time as a Magistrate and he later became Chairman of the Bench.
Mrs Le Pen is expected to win a seat in the assembly, but fail to capture more than six across the country for her party.
In the first round, the abstention rate hit a almost 60-year high of 51.3 percent and is forecast to rise to 53-54 percent in the run-off, much higher than the 44.6 percent in the last election five years ago. Nationwide, it stood at just over 35% as of 5 p.m. local time (11 a.m. ET) on Sunday, France's Interior Ministry said on its website, significantly down compared with the same time in the 2012 election.
The right-wing Republicans and their allies emerged in the exit polls as the largest opposition party, with 125 seats.
The National Front had two seats in the outgoing parliament and the only lawmaker seeking to renew his mandate, Gilbert Collard running in the southern Gard region, could lose.
Francois Baroin, who led The Republicans' campaign, said the conservatives would emphasize their differences with Macron, especially on taxes.
"This is France, not Russian Federation", far-left candidate Jean-Luc Melenchon said Friday (16 June) on Europe 1 radio.
Party could take 355 to 425 seats in the 577-seat National Assembly, the powerful lower house.
His opponent, a former bullfighter representing Macron's party got a public boost this week from visiting Prime Minister Edouard Philippe.