The attack took place in the village of Al-Hamam, according to Rami Abdel Rahman, who runs the London-based Syrian Observatory for Human Rights, and ws carried out by the Islamic State of Iraq and the Levant and the Al-Nusra Front.
It was not clear whether the bomber, who was in his 20s and nicknamed "Abu al-Qaaqaa" after one of the Prophet Mohammed's companions, was a French convert to Islam or from a Muslim family.
Tha Al-Nusra Front is one of the most effective armed groups fighting Bashar al-Assad's regime and is made up primarily of Syrians, according to Abdel Rahman, while most of the Islamic State of Iraq and the Levant's members are foreigners.
Both groups have sworn allegiance to Al-Qaeda, although there are conflicting claims on their relations with each other.
Al-Qaaqaa is not the first French national to die fighting against Assad.
A French convert to Islam was killed on 24 September and another, a 22-year-old identified as Jean-Daniel, was killed last August.
French Interior Minister Manuel Valls said last month that as many as 300 French citizens or residents were currently fighting in Syria, planning to go and fight or had recently returned.
Members of the Organisation for the Prohibition of Chemical Weapons (OPCW) started their first mission to check on the Assad regime's chemical weapons on Friday after the announcement that their organisation had been awarded the Nobel Peace Prize.