Candidates who secure 50 percent of the constituency vote on a minimum turnout of 25 percent will win in the first round.
The Ipsos Sopra Steria poll projected Macron's Republic On The Move (LREM) would win 31 percent of the vote in the first round of voting on June 11, up from 29.5 percent the last time the survey was conducted almost a week ago.
The National Front, whose leader leader Marine Le Pen lost to Macron in the presidential run-off, could secure 17 percent in the first round but drop to only five to 15 seats in the second.
His centrist Republique en Marche (Republic on the Move, REM) party, which he only founded in April 2016 as a platform for his presidential bid, now needs a clear majority in the National Assembly for him to push through the reforms he has promised.
Macron's predecessors Francois Hollande in 2012, Nicolas Sarkozy in 2007 and Jacques Chirac in 2002 all won outright majorities.
During one month in office, he's further weakened the Socialist Party and the center-right Republicans by poaching some of their leading members for cabinet positions.
France's President Emmanuel Macron waits prior to meet the President of Guatemala Jimmy Morales, at the Elysee Palace, in Paris, Thursday, June 8, 2017.
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The 39-year-old Macron was elected in May after creating a centrist political movement that took millions of votes away from the two parties that have dominated French politics for decades.
Macron's party has brushed off the accusations against Ferrand as unfounded.
While elections in the lower house of parliament's 577 constituencies can be tricky to predict, especially with a total of 7882 candidates vying for those seats, even LREM's rivals have been saying they expect Macron to get a majority. May has said she will try to form a minority government.
But Le Pen remains defiant, telling AFP this week that with other parties likely to agree to work with Macron, "we will be the only opposition force".
Macron has appealed to voters to give him a strong mandate to overhaul the labour market whose rigid rules on hiring and firing hold back the economy, according to many experts.
Jean-Yves Le Drian, a mainstream Socialist and former defense minister, is now foreign minister.
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