"Our enemy is Daesh, Islamic State, it has territory, an army and resources, so we must create this large coalition to hit these terrorists," Hollande said in televised remarks at the start of bilateral talks with the Russian leader in the Kremlin, Reuters wrote.
"I'm in Moscow with you to see how we can act together and coordinate so that we can strike this terrorist group, but also reach a solution for peace," Hollande said.
Putin said Moscow was ready to unite with Paris against a "mutual enemy" following the downing of the Russian airliner and the attacks in Paris.
However, the leaders avoided looking at each other during their brief televised exchange, underlining the still-awkward relationship between Russia and the West due to the Ukraine crisis and differences over Middle East policy.
Both Russia and France have stepped up their aerial bombing campaigns in Syria but they have different objectives.
Hollande is on a diplomatic offensive to build a common front against the militant Islamist group that has claimed responsibility for the attacks in Paris on November 13 that killed 130 people.
Islamic State has also said it downed a Russian plane on October 31 over the Sinai Peninsula in Egypt, killing all 224 people on board.