The National Assembly voted by 162-148 late on Tuesday to write a passport-stripping clause into the Constitution, despite misgivings by some lawmakers that it was too extreme, Reuters wrote.
The vote appeared to only partially defuse concerns of a broad rebellion scuttling a proposal that some, notably members of the ruling Socialist Party, consider an ineffective, symbolic measure in France's battle against terrorism.
Hollande's government launched the long process to change the Constitution after the Nov. 13 Paris attacks, for which the militant group Islamic State claimed credit.
French Prime Minister Manuel Valls welcomed the vote's result.
Asked by reporters if the tight outcome meant there was a risk the reform could fail to pass the next legislative steps to make it definitive, Valls said, "Tomorrow, we will hold another vote. I think the approval will be broader and the constitutional reform will go ahead."
A follow-up vote is scheduled for Wednesday in which the lower house is due to reaffirm the vote.
Critics have said that any law is likely to stigmatize French citizens with dual nationality, such as those from former French colonies in Africa. Under international law, governments cannot make citizens stateless.
Earlier on Tuesday, former right-wing president Nicolas Sarkozy backed the plan and criticized opponents, saying "with 130 people killed, we made a commitment never to behave like small-minded politicians in the face of such a tragedy."
France is in the process of extending until the end of May a state of emergency that was declared on the heels of the attacks.
In the run-up to Tuesday's vote, the resignation of France's justice minister over the issue and dissent among other members of the Socialist party had raised doubts about the chances of the Constitutional changes being adopted.
To change the constitution, the government's proposal will need approval by the upper house of parliament, the Senate, and then finally by both houses by a three-fifths majority, a process likely to take weeks.
Hollande is widely expected to reshuffle his cabinet in coming days in a bid to regain lost popularity.