Ankara is recalling its ambassador and freezing political visits as well as joint military projects, including exercises, Recep Tayyip Erdogan said.
The bill was passed by the French National Assembly on Thursday and is due to go before the Senate next year.
French Foreign Minister Alain Juppe has publicly opposed it.
Under the bill, those publicly denying genocide would face a year in jail and a fine of 45,000 euros (£29,000; $58,000).
Armenians say up to 1.5 million people were killed by the Ottoman Turks in 1915-16.
Ankara says closer to 300,000 people died, and that Turks were also killed as Armenians rose up against the Ottoman Empire when Russian troops invaded eastern Anatolia, now eastern Turkey.
More than 20 countries have formally recognised the killings as genocide.
According to French news agency AFP, angry crowds in the Turkish capital, Ankara, have been chanting: "We have not committed genocide, we defended the homeland.
"Wait for us France, we will come."
Speaking in Ankara, Mr Erdogan suggested the bill would create lasting damage to relations with France.
"This will open very grave and irreparable wounds," he said.
Mr Erdogan told reporters: "This is politics based on racism, discrimination and xenophobia.
"This is using Turkophobia and Islamophobia to gain votes, and it raises concerns regarding these issues not only in France but all Europe."
He said Ankara would cancel permission for French military planes to land and warships to dock in Turkey as a result of the bill, Reuters news agency reports.
Relations between the two countries are at an all-time low thanks to French President Nicholas Sarkozy's opposition to Turkey's bid for membership of the EU, the BBC's David O'Byrne reports from Istanbul.
'Inspired by European law'
The bill's author, Valerie Boyer from France's ruling conservative UMP party, said she was "shocked" at Turkey's intervention.
"My bill doesn't aim at any particular country," she said.
"It is inspired by European law, which says that the people who deny the existence of the genocides must be sanctioned."
Maurice Delighazarian, 75, lost his grandparents in 1915.
"Our ancestors can finally rest in peace," he was quoted as saying by the Associated Press news agency in Paris.
Armenian Foreign Minister Edward Nalbandian thanked the French parliament, and France's "top leadership" and its people, for the bill.
France had, he said, "once again proved its commitment to universal human values".
But Mr Juppe criticised the proposed law, which follows France's formal recognition of the killings as genocide in 2001. No penalty was attached for denial at the time.
Mr Juppe told reporters it was a critical juncture in the Middle East and he emphasised the role Turkey had been playing in the Arab Spring, as well as the strong economic ties that existed between Turkey and France.
"It [the bill] is useless and counter-productive," he said.
His disapproval appears to be in direct conflict with the tacit support that has been given by President Nicolas Sarkozy to the bill, the BBC's Christian Fraser reports from Paris.
There are some half a million ethnic Armenians living in France and their vote is considered important in next year's presidential election, our correspondent notes.