Those who oppose the hijab ban say it is the latest erosion of religious freedoms against Muslims in the country and across Europe, where other nations have introduced bans covering Islamic garments in recent years.
France banned wearing a full-face veil in public in 2011, and last month a referendum instigated by a far-right group to ban facial coverings in Switzerland won a narrow victory.
Denmark, Austria, the Netherlands and Bulgaria have also implemented full or partial bans on wearing face coverings in recent years.
What is the ‘anti-separatism’ bill and why is it being introduced?
France has a strict form of secularism and the government has said the bill – a wide-ranging crackdown on speech and actions by religious figures or organisations which are seen as subverting core values of the French republic - will help to uphold it.
The bill does not explicitly mention Islam. France's constitution prohibits discrimination on the basis of religion, meaning it must be written in a way that means it applies to all.
Christian leaders have also voiced fear the bill will impose undue limits on basic freedoms.
However the right-wing Republicans party and far-right National Rally both pushed during the drafting process for wider restrictions on the wearing of the Islamic headscarf in public, and it has been debated in a highly charged atmosphere following a series of controversies around Islam.
In October last year, French President Emmanuel Macron provoked international outrage after he denounced a trend of "Islamist separatism" that sought to create a "counter-society" rejecting secularism, equality between the sexes, and other parts of French law.
One line from a particular speech - "Islam is a religion that is in crisis all over the world" - drew especially fierce criticism overseas.
That same month, school teacher Samuel Paty was beheaded in the street by a radicalised teen of Chechen origin after showing his class cartoons lampooning the Prophet Mohammed. About two weeks after that, a 21-year-old Tunisian killed three people at a church in the southern city of Nice, further raising tensions.
The French minister for higher education sparked backlash in February from university heads after warning about the spread of "Islamo-leftism" in the country's academic institutions.
"It's an extremely strong secular offensive," Interior Minister Gerald Darmanin told RTL radio of the bill ahead of the Senate vote last month.
"It's a tough text ... but necessary for the republic."
How are Muslims reacting?
Many see the bill and the hijab ban as the latest recent move by France that unfairly stigmatises its sizeable Muslim community.
In the wake of Mr Paty's killing last year, the government used its existing powers to close several mosques and two leading Muslim organisations, the charity Baraka City and the Collective Against Islamophobia in France.
Olympic fencer Ibtihaj Muhammad – the first Muslim American woman to wear a hijab while competing for the United States in the Olympics – said the hijab ban amounted to “Islamophobia written into law”.
“This is what happens when you normalise anti-Islamic and anti-Muslim hate speech, bias, discrimination, and hate crimes,” she wrote on Instagram.
US activist Amani al-Khatahtbeh also took to social media, tweeting: “No government should regulate how a woman can dress, whether to keep it on or take it off”.
There are also concerns from the Muslim community in Australia the hijab ban will further marginalise an already vulnerable community in France and worsen tensions.
“This is an attack on the freedom of Muslims to worship their freedom of religion, and it definitely is marginalising the French Muslim community further,” Islamic Council of Victoria president Adel Salman told SBS News.
“The Muslim minorities in France and other places feel that they are being singled out, feel that they are second class citizens - that’s going to create tensions.
“The message here from the French government and leaders is that Muslims, or Muslim-ness, or Muslim identity, is not welcome.”
Mr Salman said it was worrying that countries across the world appeared to be increasingly adopting policies that target Muslims, and more may come in the future.
“We've been watching this play out in Australia and around the world with alarm, and it just seems to be escalating,” he said.
“When you have governments actually spearheading some of these policies … this is going to encourage others in those societies actually do the same.”