"When you see that the conflict, which started as a civil war, transformed into a regional war with the involvement of international forces, [then] the risk of escalation runs very high," Fabius said in an interview with the French radio broadcaster Europe 1.
He added there was a risk of the conflict turning into a confrontation between Sunnis and Shiites, the two main branches of Islam.
Syria has been in a state of civil war since 2011, with forces of the country's President Bashar Assad fighting opposition factions and numerous extremist groups, including Islamic State (ISIL) and the Nusra Front.
Since 2014, a US-led coalition has been bombing IS terrorist positions in Syria without the approval of the UN Security Council or the Syrian authorities.
Russia, Syria, Iran and Iraq agreed in September to cooperate on security and intelligence sharing in Syria and set up an information center in Baghdad to coordinate their efforts.
On Wednesday, Russia launched its first airstrikes on IS positions in Syria at Assad's request.