The new government is set to take power in January in Tripoli following a fragile UN-brokered accord reached earlier this month.
Fabius phoned Sarraj to assure him that France will "be at the side of the Libyan people to overcome the challenges confronting the country, starting with the securing of the capital, the return of stability and the fight against terrorism," his office said in a statement.
France will provide emergency medical aid to Benghazi, a city in the east of Libya where fierce fighting continues between competing militias.
But it has created sharp divisions within Libya's two competing legislatures, and will face huge challenges in dealing with the multi-faceted civil war in the country, which includes an offshoot of the Islamic State group.