The case went to a Paris appeal court on Monday, a lower court having declared itself incompetent to hear it because it concerned France's foreign policy.
The plaintiffs, all Syrians, claim that several statements by Fabius stoked the Syrian conflict in 2012.
They also cite a quotation in Le Monde newspaper when Fabius reported that the Syrian opposition coalition and "all the Arabs" opposed the US decision to put al-Nusra on its terrorist list because "they are doing a good job on the ground".
Legal officials on Monday asked the appeal court to endorse the lower court's decision on the grounds that the statements concerned French foreign policy and could not be taken out of that context.
For the plaintiffs' lawyer, Damien Viguier, they were "stirring up civil war" and "personal misconduct distinct from the government's policy".
They want Fabius condemned for "provocation to commit mass crimes" and want a symbolic euro in compensation.
A similar case brought before the Court of Justice of the Republic, which judges accusations by ministers while there in office, was closed in January 2014.