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Deputies in the National Assembly voted 106-19 for the bill, which if signed into law, would punish denial with a maximum one-year prison term and a fine of up to €45,000 (£30,000).
After the vote, the French government stressed that it valued close ties with Turkey and said that it would continue to oppose the motion, which needs to be ratified by the upper house Senate.
"This is just the beginning of a long legislative process. At each stage, the government will continue to make known its position on this proposed Bill, which appears unnecessary and untimely," a Foreign Ministry statement said.
"We are very attached to dialogue with Turkey as well as the solid ties of friendship and cooperation which unite our countries."
Today's vote caused outrage in Turkey where it has dominated the front pages, with some newspapers reporting that thousands of Turks have promised to go to France and deny genocide in hopes of getting arrested if the bill passes.
The Turkish foreign ministry said the vote had dealt a "severe blow" to relations between France and Turkey and analysts warned that it would complicate Turkey's efforts to secure membership of the European Union.
In a statement the ministry said: "French-Turkish relations, which have developed over centuries... have been dealt a severe blow today as a result of the irresponsible false claims of French politicians who do not see the political consequences of their actions."
Turkey denies accusations of genocide and says that 300,000 Armenians, and at least as many Turks, died in civil strife when Armenia took up arms for independence as the Ottoman Empire fell apart after the First World War.
However, Armenians say that up to 1.5 million of their ancestors were slaughtered in orchestrated killings, which they maintain can only be seen as genocide.
France has one of the largest Armenian communities in Europe, up to 500,000 people, and with elections seven months away many MPs from the ruling Union for a Popular Movement (UMP), are not expected to opposing it.
Turkey also faces presidential and parliamentary elections next year and nationalism has been on the increase. "Given the proximity of elections, the Turkish parliament can only react aggressively [to the French vote]," said economist Lars Christensen of Danske Bank in Copenhagen.
"It can only worsen prospects for EU accession and will move the Turkish population even further from pro-EU sentiment. The closer we come to Turkish elections, the more risks we factor into Turkey."
Turkey began membership talks with the EU this month, but the process could take more than a decade and even then its entry is not guaranteed.
Ali Babacan, Turkey's chief negotiator, said the French Bill flew in the face of freedom of expression. He said: "This is violating one of the core principles of the European Union, which is freedom of expression. Leave history to historians."
A spokeswoman for the commission said that talks on Turkey's possible entry into the European Union did not include recognition of the Armenian killings as genocide.
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