The amendment, including a hotly contested measure to strip convicted terrorists of their French nationality, was passed by the National Assembly with 317 votes for to 199 against, clearing a first hurdle towards adoption.
The package must now gain the support of the Senate, or upper house of parliament, and then three-fifths of the Congress, the body formed when both houses of France's parliament come together to debate revisions to the constitution.
Prime Minister Manuel Valls said he was satisfied with the result. He said he was "sure" the amendments would receive a majority in the Congress.
The stakes were high for President Francois Hollande, who announced in the emotional aftermath of the shootings and suicide bombings that killed 130 people in Paris in November that he wanted to revise the constitution to toughen the fight against terror.
If the measures had fallen at the first stage, it could have dealt a fatal blow to Hollande's ambitions of re-election in 2017.
Valls had on Tuesday warned lawmakers from his Socialist Party that voting against the measures would "put the government in difficulty and leave the president in a minority".
The fact that the move to strip terror convicts of their nationality barely scraped through by 162 votes to 148 in a separate vote on Tuesday suggests the collective package faces many more obstacles.
Writing on his Twitter account ahead of Wednesday's vote, right-wing politician Alain Juppe, a former prime minister seen as the frontrunner in next year's presidential election, dismissed the reforms as "pointless" and said they "divide all the parliamentary groups -- to be avoided!"
Cecile Duflot, a member of the green EELV party and a former minister in Hollande's government, urged her fellow MPs to "resist the blackmail" posed by the nationality measure.
Another of the proposed measures would enshrine in the constitution the state of emergency currently in force, giving greater powers to security forces.
Rights groups and left-wing lawmakers say they believe police are abusing the additional powers, rounding up suspects with little proof.
But it is the nationality measure that has deeply divided Hollande's party, notably prompting the resignation of Christiane Taubira as justice minister last month.
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In addition, Hollande's former prime minister Jean-Marc Ayrault has publicly condemned the proposal.
But the government insists the measures are necessary as France faces a continued high threat from jihadist attack.
Valls said Tuesday the terrorist threat was "without doubt more serious than before November 13".
The Islamic State group claimed responsibility for the carnage in Paris, saying it was in response to French air strikes against the group in Iraq and Syria.
It was the second time in a year that jihadists had struck at the French capital. In January 2015, gunmen attacked the offices of the satirical newspaper Charlie Hebdo and a Jewish supermarket.