"There is an opening, so to speak, with the Russians. We think they are sincere and we must bring together all our forces," Fabius told France Inter radio, as reported by AFP.
Relations between France and Russia have deteriorated since last year's Ukraine crisis.
But both countries have suffered major terror attacks at the hands of ISIL in recent weeks -- the coordinated gun and bomb attacks last Friday in Paris, and the bombing of a Russian passenger jet over Egypt last month.
President Francois Hollande called this week for the "bringing together of all those who can realistically fight against this terrorist army in a large and unique coalition", while his Russian counterpart Vladimir Putin ordered his navy in the Mediterranean to establish contact with its French counterparts and work together "as allies".