The bill sets a punishment of up to one year in prison and a fine of 45,000 euros ($59,000) for those who deny or "outrageously minimize" the alleged genocide of Armenians in eastern Anatolia during the final years of the Ottoman Empire, putting such action on par with the denial of the Holocaust.
About 50 lawmakers were present during the debates on the bill. The majority of the lawmakers, including Patrick Ollier, the government minister in charge of relations with parliament who addressed the session on behalf of the government, opposed an amendment proposal which said academic and scientific studies on history should be exempt from punishment set by the bill. The amendment proposal was eventually withdrawn by the lawmaker who presented it.
The measure now needs to be passed in the senate, the upper house of parliament, to go into effect.
Turkey, which vehemently rejects the term "genocide," has campaigned to get France to abandon the legislation, threatening to withdraw its ambassador and warning of "grave consequences" to economic and political ties.
France formally recognized the killings as genocide in 2001, but provided no penalty for anyone denying that.
Lawmakers denounced what they called Turkey's propaganda effort in a bid to sway them.
"Laws voted in this chamber cannot be dictated by Ankara," said Jean-Christophe Lagarde, a deputy from the New Center party, as Turks demonstrated outside the National Assembly ahead of the vote.
The bill's author said she was "shocked" at the attempt to interfere with the parliament's work.
"My bill doesn't aim at any particular country," said Valerie Boyer, a deputy from the ruling conservative UMP party. "It is inspired by European law, which says that the people who deny the existence of the genocides must be sanctioned."
President Nicolas Sarkozy's conservative government backed the measure despite the ire - and threats - of Turkey.
An initial bid to punish denial of the Armenian genocide failed earlier this year, killed by the Senate five years after it was passed by the lower house.