Mamlouk, one of Bashar al-Assad's most senior advisers, was targeted by the order alongside Jamil Hassan, the head of Air Force Intelligence who is already the subject of a German warrant, the sources said.
Another senior Air Force Intelligence official, Abdel Salam Mahmoud, was also named in the French order, one of the sources said.
The warrants stem from a long-running case involving two French-Syrian nationals who were arrested in Syria in November 2013 and had disappeared since.
Damascus confirmed in August 2018 that the father and son, Mazen and Patrick Abdelkader Dabbagh, were dead, the sources said. They include a lawyer for their family, Clemence Bectarte, who said the warrants were issued in mid-October.
Prosecutors in Paris had already opened a probe into the pair's disappearance, starting with a preliminary investigation in 2015, and had found that their house in Damascus had been raided by intelligence officials, the judicial source said.
The French warrants bring charges including collusion in torture, forced disappearances, crimes against humanity and war crimes against the Syrian officials.
Germany - which has universal jurisdiction over war crimes, meaning it can prosecute and try crimes committed abroad - has also taken similar steps, issuing an arrest warrant in June for Air Force Intelligence official Hassan.
Efforts to prosecute members of the Assad government have repeatedly failed because Syria is not a signatory of the Rome Statute of the International Criminal Court (ICC) in the Hague. Russia and China have also vetoed attempts to give the ICC a mandate to set up a special tribunal for Syria.