French Foreign Minister Jean-Yves Le Drian said before the meeting in Paris with his Turkish counterpart Mevlut Cavusoglu that "we have to know what happened" to the two men.
He said he had met with their families and had "strongly urged the Turkish authorities to shed full light on this situation".
"We are sadly working under the hypothesis of a kidnapping," Le Drian said, adding that French President Emmanuel Macron was being updated regularly about the case.
A third French national, identified as Alexandre Berceaux, was also taken hostage but later released by militants.
Cavusoglu said Turkey was working closely with France to find the two men. "We will share all information we have, and we will do our best to bring them back home safely," he added.
French and Turkish officials are working together on all aspects of the case, Le Drian said, adding that there were no negotiations being conducted for their release at this stage.
"What I am asking is to know what happened, where they are," he said. "We're not in the negotiation phase yet."
Turkish Foreign Minister Mevlut Cavusoglu and his French counterpart Jean-Yves Le Drian hold a joint press conference in Istanbul on September 3, 2017. (AFP)
France has more than 30,000 nationals living in Turkey, according to the French embassy. The country is also home to about 500,000 people of Turkish origin.
French national Mehmet Yilmaz was arrested earlier this year after he appeared in a video threatening to attack Turks living in France unless Islamist preacher Fetullah Gulen was released from prison. He was later sentenced to six months' imprisonment for "terrorist propaganda".
Another Frenchman suspected of links with Gulen's network was taken into custody last month during a raid on an apartment building in Istanbul's Fatih district where he had been under police surveillance for some time.