France also wants the perpetrators of the deadly chemical weapons attack tried before the international justice system, Fabius said.
Iran, a longtime Syria ally, welcomes the Russian initiative "to stop militarism in the region."
China, also an ally of Syria, says it welcomes and supports the proposal.
The opposition Free Syria Army says Russia's proposal is nothing more than a stalling tactic.
"Here we go again with the regime trying to buy more time in order to keep on the daily slaughter against our innocent civilians and to fool the world," said Louay al-Mokdad, a spokesman for the group.