The draft law has been under consideration for some time but recent Islamist attacks pushed it up the agenda.
Paty’s murder was one of three attacks that outraged France. Three people were killed in stabbings in a Nice church in October.
Two people were stabbed and seriously hurt in September in Paris near the former offices of Charlie Hebdo magazine, where Islamist militants carried out a deadly attack in 2015.
President Macron is a staunch defender of French Republican values including state secularism. He has described Islam as a religion “in crisis” and defended the right of Charlie Hebdo to publish cartoons of the Prophet Mohammed.
France has an estimated five million Muslims, Europe’s largest Muslim minority.
What has the reaction been?
Mr Macron has become the target of sharp criticism in several Muslim-majority countries.
Relations with Turkey, already strained, were further undermined with President Recep Tayyip Erdogan describing the legislation as an “open provocation” and saying Mr Macron was “mentally ill”.
Demonstrations have been held in Pakistan, Bangladesh and Lebanon.
The US envoy on religious freedom, Sam Brownback, was also critical, saying: “When you get heavy-handed, the situation can get worse.”
In France itself, some left-wing politicians have expressed concern that the legislation could be seen as stigmatising Muslims.
Le Monde newspaper says it could also antagonise other religious groups who practise home-schooling.
But the BBC’s Lucy Williamson in Paris says pressure has grown on President Macron to act.
Tackling Islamist influence in the name of French secularism may be popular at home, but it’s still a delicate operation for the state, she adds.