France firmly backs the Syrian rebels and has strategic and historic interests in the region. It urged military action after a chemical attack on Aug. 21 that Paris and Washington blame on Assad's government.
In contrast, China and Russia have consistently blocked resolutions at the U.N. Security Council aimed at sanctioning Assad's regime.
After Sunday's meeting, the French foreign minister said the deal on destroying Syria's chemical weapons was "a significant step forward, but it's a first stage."
"On one hand, we are going to move forward with the destruction of chemical weapons bravo but on the other hand, hundreds of deaths every day are mounting in Syria and that's also what we must tackle, that is to say find a political solution to the Syrian crisis," Fabius said.
He said he would discuss the agreement and its implementation at a meeting Monday in Paris with U.S. Secretary of State John Kerry and British Foreign Secretary William Hague. On Tuesday, he will meet with his Russian counterpart, Sergey Lavrov, in Moscow.
Fabius also said a report by U.N. inspectors on last month's chemical weapons attack on the outskirts of Damascus would be published Monday.