The bill still needs the approval of the Senate and the president before it can take effect.
It proposes penalties of up to a year in jail and a €45,000 ($A75,200) fine for anyone denying that the 1915-1917 massacres were genocide.
The draft law has enraged Turkey, which rejects the use of the term genocide in the sensitive Armenian issue.
Turkey’s foreign ministry has condemned the French bill and said that it has put a strain on relations between the two countries.
"Turkish-French relations, which have been meticulously developed over the centuries, took a heavy blow today through the irresponsible initiatives of some short-sighted French politicians,"
But Armenia's foreign minister, Vartan Oksanian, has welcomed the French approval of the bill.
He described it as "a natural continuation of France's principled and consistent defence of human and historic rights and values."
The French Prime Minister Dominique de Villepin however tried to distance his government from the bill saying it was "not a good thing to legislate on issues of history and of memory."
The proposed law was introduced by MPs of the opposition Socialist Party.
Catherine Colonna, France's minister for European affairs, said the government of President Jacques Chirac was "not favourable" to the law.
Economic stake
Christine Lagarde, minister for foreign trade, highlighted the "major economic stake" that her country has in Turkey.
She said France risked jeopardising billions of euros' worth of trade with the country, while the EU said the bill could interfere with Turkish plans to join the European bloc.
"With this draft law, France is unfortunately losing its privileged status with the Turkish people," a Turkish foreign ministry statement said.
Ankara claims that the law flouted European laws on freedom of expression.
Turkish business and consumer groups called for a boycott of French goods and for French companies to be sidelined from public tenders.
Turkey's economy minister in Brussels said his country did not plan an economic boycott.
Region divided
Authorities in Turkey's close ally Azerbaijan, an ex-Soviet republic bordering Armenia, echoed Ankara's outrage.
"This decision damages France itself, the cradle of democracy," said Novruz Mamedov, foreign affairs advisor for Azerbaijan's presidential administration.
Turkey's historic rival Greece meanwhile criticised what it called Turkish "threats" to France over the draft law.
"Threats or insinuations... do not befit a country on the road to joining the European Union," foreign ministry spokesman George Koumoutsakos said.
Turkey last year opened talks with Brussels with a view to joining the European political bloc.
The EU's executive arm, the European Commission, criticised the French bill, saying it could harm reconciliation efforts necessary for Turkey to join.
Varying accounts
Ankara says 300,000 Armenians and at least as many Turks died in civil strife during World War I.
Turkey claims Armenians took up arms for independence and sided with invading Russian troops as the Ottoman Empire fell apart.
But Armenians claim up to 1.5 million of their ancestors were slaughtered in orchestrated killings that they say can only be seen as genocide.
An association representing the Armenian disapora in Europe, the Brussels-based Euro-Armenian Federation, in a statement welcomed the bill's approval, calling it a "historic step forward".
Patriarch speaks out
The spriritual leader of Turkey's Armenian minority joined the chorus of criticism that greeted Thursday's decision.
Patriarch Mesrob II said the French move "sabotaged" efforts at dialogue between Turks and Armenians and said he feared reprisals against the 80,000-strong Armenian community in Turkey.
“The French, who in the past put various obstacles in the way of Turkey's bid to join the European Union, have now dealt a serious blow to the already limited dialogue between Turkey and Armenia," he said in a statement carried by Anatolia news agency.