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Tereos, which denies the claims, is accused of "acts of terrorism and complicity in acts of terrorism", according to documents from the anti-terror prosecutor's office seen by AFP.
The plaintiffs allege that Tereos had vowed to halt deliveries to conflict zones after an EU-mandated NGO found dozens of the company's bags containing sorbitol in a warehouse of the Islamic State (IS) group in Iraq after the liberation of Mosul in late 2016.
Sorbitol, when mixed with potassium nitrate, can be used to make rocket propellants.
Confronted with the findings by the Conflict Armament Research (CAR) NGO, Tereos admitted that some 45 tonnes of French-produced sorbitol had already vanished in Turkey in 2015 and resurfaced a year later in IS basements in Syria.
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When CAR released its report in December 2017, Tereos insisted it had "suspended its sorbitol supplies to so-called high-risk areas" shortly after the Mosul discovery.
However, the plaintiffs say an internal company investigation has shown that two shipments of sorbitol were made to Syria in February and July 2017.
"Despite Tereos' awareness of the use of sorbitol as a weapon of war, the company knowingly continued to supply this raw material to a terrorist group," the plaintiffs said in the documents.
Lawyer Jade Dousselin said her clients had been "stunned" by the allegations. "It's a shock and a betrayal of Tereos as a flagship of our agricultural economy," she said.
The company said its sales to Syria had been "legal".
"We stopped them when we discovered that the product was being misused," Tereos told AFP on Tuesday.