Speaking at a press conference Fabius said the resolution will be presented later on Tuesday.
Fabius said the resolution would require Assad to offer full disclosure of his chemical weapons programme and that his arsenal be dismantled “without delay”.
The foreign minister says the resolution will also demand that the perpetrators of the chemical attack in Damascus that left scores dead, be handed over to the International Criminal Court to face justice.
If the terms are not adhered to then the resolution will commit the UN to "serious measures", Fabius said.
Speaking earlier in the day about Russia's propsosal that Bashar al-Assad hands over the chemical arms to international observers Fabius insisted that the Syrian president "commit himself without delay" to the elimination of his country's chemical weapons arsenal.
"The proposal of Russian Foreign Minister Sergei Lavrov merits close examination," Fabius said, demanding that Assad "commit himself without delay to put his chemical arsenal under international control and to let all of it be destroyed".
Assad "must commit without delay to put his entire chemical arsenal under international control and have it destroyed", he said adding that this "operation must be carried out on the basis of a binding Security Council resolution, with a short timetable and firm consequences if he does not respect his commitments."
And the International Criminal Court must get involved because "those responsible for the August 21 chemical massacre must no go unpunished".
"We demand precise, quick and verifiable commitments by the Syrian regime," he added.
French Defence Minister Jean-Yves Le Drian also said on Tuesday that international pressure had worked, after a plan emerged to head off punitive US air strikes on Syria by destroying the regime's chemical weapons.
"It's an opening. It must be seized upon and Bashar al-Assad's regime must formally respond and firmly engage to it, and it must be implemented quickly," Le Drian said. "The international pressure worked."German Chancellor Angela Merkel said she hoped "action" would follow Russia's proposal, and that it was not just a way to buy time.
"Today there was an interesting proposal from Russia, which called on Syria for the first time to place its chemical weapons under international control," said Merkel on German public television speaking to a group of German voters.
"If this is followed by action and not about buying time and this materialises, then Germany will push for that road to be followed," she said.
"Everything must be tried to achieve this without military intervention," she added, referring to the threat of US-led military action to punish the Assad regime for its alleged chemical attack.
Merkel, who is seeking re-election for a third term in September 22 poll, also again stressed that "Germany will under no circumstances" be part of any military strike.
France and the United States claim growing international support for military strikes to punish the Syrian regime for the alleged chemical attack, while Russia, Syria's staunchest ally, on Monday seized the diplomatic initiative with its plan to head off the threat of US military strikes.