Mr Macron’s centrists were predicted to take just 135 seats, almost half the 246 MPs it currently has.
The hard-Left coalition would also lose support, taking an average of 68 seats compared to 131 two years ago.
Les Republicains, once one of France’s two major establishment parties, would lose 10 seats, dropping to about 53 MPs.
The party, led by Eric Ciotti, commissioned the poll to gauge the risks and rewards of voting to censure the government.
This could lead to the dissolution of the French parliament and assembly elections, although Mr Macron would remain as president.
“We wanted to take the pulse of the country,” a Republicain source told the L’Obs newspaper.
The insider said that the poll showed an “encouraging stabilisation” for the once-dominant party, which has provided a string of presidents, and pointed to the collapse in support for the hard Left.
But the polls also convinced the party leadership not to call early elections. Although a minority force, it could topple the government if it joined forces with National Rally and the Left.
National Rally is predicted to trounce Mr Macron’s centrists in the European Parliament elections in June, with polls showing it taking more than 30 per cent of the vote and being the biggest French party in the pan-EU vote.
Ms Le Pen is reported to view the European elections as a springboard for her next tilt at the Elysee.
Mr Macron must step down as president in 2027 and cannot run for a third term.