The sudden closures of the missions came with Turkey on edge after the triple suicide attack last month on Istanbul's main airport which was blamed on Islamic State (IS) jihadists.
"The Embassy of France in Ankara, as well as the Consulate General in Istanbul will be closed from today July 13, 1.00 PM (1000 GMT), until further notice," the embassy said in a statement after scrapping the July 14 receptions at the missions on security grounds.
France's consulate in Istanbul, its embassy in Ankara and its mission in the Aegean city of Izmir were all to have held celebrations marking the July 14 French national day.
French Foreign Minister Jean-Marc Ayrault said he had personally taken the decision to cancel the receptions after receiving information about a "real and concrete threat".
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"The information which we received, and was confirmed by an exchange with the Turkish services, showed that there was a real and concrete threat," he told reporters in Paris, without giving any details.
Turkey's Deputy Prime Minister Numan Kurtulmus suggested, in an interview with the A Haber TV channel, the threat could be from IS as the jihadists have previously targeted France and could do so again,
"It is known France is a target for Daesh. Across the world, there is a potential for attacks against French targets. I hope we do not face this in Turkey but all precautions are being taken," he said, using the Arabic acronym for IS.
The June 28 attack on Ataturk International Airport raised new alarm over the security of foreigners in Turkey after a spate of attacks this year blamed on jihadists and Kurdish militants.