Under the new provision, buying sex acts will be punishable by a $A2256 (1500 euro) fine. Repeat offenders risk a fine of $A5640 (3750 euros). Alternatively, a course will be proposed to make them aware of the risks involved in the sale of sex.
Dozens rallied both for and against the bill as debate began in the lower house, the National Assembly, which is expected to vote on the sex bill's other provisions on Wednesday.
Prostitution is allowed in France, but soliciting, pimping, and the sale of sex by minors are prohibited.
The government says the bill is aimed at preventing violence against women and protecting the large majority of prostitutes who are victims of trafficking gangs.
But critics warn that it would force sex workers further underground and put them in greater danger.
Starting the debate, Maud Olivier, one of the people behind the bill, blasted the "hypocrisy" of critics.
"One prostitute declares herself free and the slavery of others becomes respectable and acceptable?" the socialist MP asked parliament.
"How can you find glamorous the 10 to 15 penetrations a day endured by prostitutes for economic reasons with dramatic consequences on their health?"
Women's Rights Minister and government spokeswoman Najat Vallaud-Belkacem told the politicians, "France is not a country that welcomes prostitution".
"The question is not sexuality. We are not here to be a moral police ... the question is about money that feeds pimping," she said.
The head of the parliamentary commission created for the bill, Guy Geoffroy, also defended the proposition, saying it "advanced women's rights".
As the session got under way, supporters and opponents of the bill rallied outside the parliament.
"You sleep with us and you vote against us," shouted a group of about 150 prostitutes, many of whom wore red or white masks.
About 50 supporters of the bill, including feminists and others, rallied nearby, holding up a banner reading: "Together for the abolition of prostitution."
There are an estimated 20,000-plus sex workers in France, many from eastern European countries such as Bulgaria and Romania as well as African nations such as Nigeria and Cameroon, and China and South America.
According to the interior ministry, foreign prostitutes make up 80 to 90 per cent of all sex workers in France, a vast majority of whom are victims of trafficking rings.
The bill takes inspiration from Sweden, where a similar law punishing clients has reduced street prostitution by half over the past decade.
But critics insist that shifting the focus onto clients will only force prostitutes to work even more covertly.
If approved, the bill will move on to the upper house, the Senate.
