Fabius said the coalition should not battle IS to the exclusion of supporting rebels fighting President Bashar al-Assad's regime, which he said had deliberately fuelled the jihadists' rise.
"After Kobane, we must save Aleppo," Fabius said, referring to a Syrian border town where Washington has carried out dozens of air strikes with the support of Arab allies to help Kurdish forces ward off a weeks-long IS assault.
France is involved in strikes against IS militants in Iraq but has so far kept out of the air campaign in neighbouring Syria, where it has hoped to support moderate rebels without resorting to military action that could help the Assad regime.
"The city is almost entirely encircled," Fabius wrote of the rebels in Aleppo.
"The regime is seeking to destroy the resistance through cold and hunger," he said in an article published by The Washington Post, France's Le Figaro and pan-Arab daily Al-Hayat.
"Some 300,000 Aleppans are holding on, threatened with the same death and destruction that the regime has inflicted on Homs and the suburbs of Damascus."
Rebels seized most of the east of Aleppo in July 2012, confining government forces to the west, but they have come under renewed assault in recent months.
"Assad and Daesh are two sides of the same barbaric coin," Fabius said, using the Arabic acronym for IS.
"Assad largely created this monster by deliberately setting free the jihadists who fuelled this terrorist movement. This was part of his underhanded effort to appear, in the eyes of the world, as the sole bulwark against terrorism in Syria."
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SUPPORT FOR MODERATE REBELS
Fabius said France would not resign itself to the breakup of Syria and would work towards supporting moderate rebels in Aleppo and protecting its civilian population, without detailing how.
"Abandoning Aleppo would mean condemning Syria to years of violence. It would mean the death of any political future," he wrote.
His article echoed the words of French President Francois Hollande on Friday, who described Aleppo as "key" to the conflict.
It also comes after sustained criticism of the coalition campaign in Syria from NATO ally Turkey, which has refused to take part in action in its southern neighbour until Washington draws up a broad strategy to deal with both IS and the Assad regime.
Washington said in response to Fabius's op-ed that the US strategy had not changed.
US Secretary of State John Kerry on Tuesday was headed to Paris for talks with Fabius, during which the fight against Islamic militants was set to be among the top agenda items.
"I will say that if the French want to take military action in Syria, which they have not to date, we would certainly welcome having the conversation with them about what contributions they'd like to make," State Department spokeswoman Jen Psaki told reporters.