The debate was pushed back to Monday evening because of the introduction of a short debate on Friday night's air strikes on Syria, which was obligatory under law but would not lead to a vote.
The immigration debate is due to last all week and could be acrimonious.
Despite some changes at committee stage, about 1,060 amendments are expected to be tabled, some of them by members of President Emmanuel Macron's Republic on the Move (REM) party.
France received 100,000 asylum requests last year, a 17.5 percent rise on 2017.
In February Toubon criticised a "massive rise" rise in the number of children in detention - a record 275 in mainland France in 2017.
NGOs that work with migrants have slammed the bill for being too repressive and rights ombudsman Jacques Toubon lost his temper with ruling party MPs during a hearing last week when they accused him of a "caricatural vision".
"If fundamental rights are caricatural, then there's a problem," snapped the former justice minister.
"Logic of fear"
While the mainstream right judges the bill timid and soft and National Front leader Marine Le Pen claims it will "speed up" immigration, the left has dubbed it "pointless and dangerous" and claims it "surfs on the logic of fear".
The Socialist Party claims it is "turning its back on our constitutional principles" while the hard-left France Unbowed has called for an "outbreak of republican and humanist convergence" to oppose it.
The most controversial proposals are:
Reducing the time allowed to lodge an asylum request to 90 days;
Reducing the time allowed to appeal against a decision to 15 days;
Prolonging the time of detention awaiting deportation from 45 to 90 days;
Allowing children to be detained, if they are accompanied by their parents;
Prosecuting campaigners who help migrants enter France as people smugglers, the so-called "crime of solidarity".
REM MPs revolt
The France Unbowed appeal for convergence is in part a pitch to ruling party dissidents.
Macron's party was only formed during last year's presidential campaign and recruited members from the Socialist Party and the mainstream right, as well as individuals new to politics.
Some see aspects of the bill as a betrayal of their liberal principles and members of the ruling party have tabled 200 amendments.
Former Socialist Jean-Michel Clément has said he will vote against the bill because of its "repressive logic", while others say they will abstain if amendments are not made.
This is the first serious division in the Macronists' ranks and it has left party leaders wondering how to deal with the dissidents.
REM parliamentary leader Richard Ferrand last week called on them to withdraw their amendments and hinted that rebels could be expelled, declaring he was ready to "break some eggs if needs be".
While conceding that discipline was Ferrand's job, REM general delegate, Christophe Castaner, was more conciliatory, saying he was against witch-hunts while appealing for party solidarity.
Amendment on solidarity possible
In a much-publicised television interview on Sunday, Macron defended the bill, declaring that "France cannot take in all the misery of the world", echoing a famous remark by former Socialist prime minister Michel Rocard.
"We are faced with an unprecedented phenomenon that is going to last," he said.
But he conceded that the crime of solidarity clause could be amended.
"Sometimes there are men and women who save people's lives," Macron said. "Our law must be adapted so that they are not convicted."
But there are also people "who consciously or unconsciously help traffickers", he insisted. "I don't want them to be let off because what they are doing is seriously wrong."