The legislation, which criminalizes illegal border crossings and aims for quicker deportation of those deemed economic migrants, has sparked widespread anger from NGOs who have branded it repressive.
The government says the law balances "efficiency" with "humanity," offering faster asylum to refugees found to have fled conflict or repression.
But it has opened divisions in the left-right coalition that newcomer Macron set up when he came to power in May, with even some members of his Republic On The Move (LREM) party breaking ranks to criticize it.
"The most vulnerable will be punished," said Jean-Michel Clement, a lawmaker who joined the centrist LREM after switching from the Socialists.
"It's not forbidden to put a little humanity into a draft law."
Some workers at France's refugee protection office, OFPRA, were going on strike to protest the bill on Wednesday, branding it "an unequivocal departure from France's tradition of asylum."
They join staff at the asylum court that have been on strike for nine days over their working conditions, with immigration lawyers also raising concerns over aspects of the draft law.
The bill will be presented to the cabinet Wednesday before being tabled in parliament in April.
While left-wingers see it as too punitive, the right have labeled it too lax.
Macron has come under pressure to toughen his stance after winning power in an election in which far-right leader Marine Le Pen won 34 percent of the vote, capitalizing on concerns over immigration.
France received a record 100,000 asylum applications last year.
The government has defended the bill as "balanced" and said it is considering proposals on how to better integrate newcomers, including doubling the number of hours of French lessons they get and allowing asylum seekers to work.
The bill also aims to cut the average waiting time on asylum applications from 11 months to six, although staff at the asylum court have raised concerns that the tighter turnaround on cases will make it more difficult to appeal.
Plans by Interior Minister Gerard Collomb to carry out immigration checks in homeless shelters have also come under fire in recent weeks.