Fabius told a UN Security Council debate that an "action charter" was needed to address the violence that saw 20 Coptic Christians beheaded in Libya last month.
"The danger is that minorities will disappear entirely," Fabius said. "The international community must not let that happen."
Islamic State militants in Iraq, Syria and Libya have targeted religious minorities in attacks, notably Yazidis in a campaign that UN investigators have said probably amounts to genocide.
Iraq was home to 1.4 million Christians in 1987, but only 400,000 remain, Fabius said.
The foreign minister called for more humanitarian aid to help minorities return to their homes and said coalition forces must make protecting religious groups a "primary goal."
Vian Dakhil, a Yazidi member of the Iraqi parliament, asked the council to formally adopt a resolution declaring the violence targeting her community as a genocide.
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More than 420,000 of Iraq's 600,000 Yazidis have been forced from their homes and are living in camps, Dakhil said.
Religious minorities have been on the "frontline" in the fight against the Islamic State, which she branded "the most dangerous terrorist organization in the world.
"More than 2,000 Yazidis have been slaughtered in cold blood by ISIL (IS) for no reason except that we are Yazidis and we profess a religion that is different from ISIL," Dakhil said.
"Our women are being raped. Our girls are being sold. Our children are taken to places, we don't know for what," she said.
Fabius called for prosecutions before the International Criminal Court, a move that was blocked by Russia and China last year when the Security Council sought accountability in Syria.
UN rights chief Zeid Ra'ad Al Hussein urged the 15-member council to overcome differences and refer Iraq and Syria to the ICC.
"The delicate mosaic is being shattered, and this Security Council must take action unanimously and decisively to end the conflicts and refer Iraq and Syria to the ICC," said Hussein.