US Secretary of State John Kerry declared the Security Council resolution sent "a clear message to all concerned that the time is now to stop the killing in Syria" and UN Secretary-General Ban Ki-moon hailed it as a "very important step" in attempts to end the conflict.
Once the resolution was passed, Fabius relaunched the diplomatic offensive against the Syrian president.
"How can somebody bring together a whole people when he has massacred so many of them?" he asked.
While Assad remains in power a "real and lasting reconciliation between the population and the Syrian state seems out of reach", he went on, calling for a transitional authority with full executive powers and control of the military and security services.
US defence chief Ashton Carter on Saturday visited the French aircraft carrier Charles De Gaulle, on mission in the Persian Gulf as a base for planes bombing positions of the Islamic State armed group in Iraq and Syria.
It is the first time a US defence secretary had visited the ship.