Radio station Europe 1 said its reporter, Didier Francois, and photographer Edouard Elias had gone missing as they were headed for the northern Syrian city of Aleppo.
Hollande, on a three-day visit to Japan, said contact with the two had been lost.
"I demand the immediate release of these journalists because they do not represent any state. These are men who have worked so the world can get information... Journalists must be treated as journalists, he told a news conference alongside Japanese Prime Minister Shinzo Abe.
Hollande declined to provide further information on the journalists so as not to endanger their lives.
A Europe 1 spokesman said French auhorities were "doing everything to provide us with information".
Four Italian journalists were kidnapped in Syria in April and were released after a little more than a week in captivity.
Another Italian journalist, Domenico Quirico, who went missing in Syria two months ago, spoke to his wife by telephone on Thursday, according to his Turin-based newspaper la Stampa.
Syrian government troops and their allies have won a string of successes in recent weeks, boosting Syrian President Bashar al-Assad at a time when the United States and Russia are struggling to organise a peace conference aimed at ending the civil war, which has killed more than 80,000 people.(*)
Editor: Heru Purwanto
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