Paris prosecutors opened a preliminary inquiry on September 15 into alleged crimes committed by the Syrian government between 2011 and 2013, the source told AFP.
The French investigation is largely based on evidence from a former Syrian army photographer known by the codename "Caesar," who defected and fled the country in 2013, bringing with him some 55,000 graphic photographs.
Foreign Minister Laurent Fabius said France had a "responsibility" to take action.
While Assad is unlikely to ever take the stand in a French court, the inquiry could add to political pressure on the Syrian leader in the midst of a diplomatic row between the West and Russia and Iran over his fate.
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The Syrian conflict has taken centre stage at the UN General Assembly, where US President Barack Obama and his Russian counterpart Vladimir Putin have clashed over how to bring an end to Syria's civil war.
Syria's four-year war has killed more than 240,000 people and Western diplomats have accused Damascus of killing more Syrians than IS by dropping barrel bombs -- charges the government denies.
The brutal conflict has also displaced millions of people, a key driver behind Europe's refugee crisis.
The photographs that Caesar brought out of Syria show people with their eyes gouged out, emaciated bodies, people with wounds on the back or stomach, and also a picture of hundreds of corpses lying in a shed surrounded by plastic bags used for burials.
The Syrian government has branded the report "political".