The call signalled a thaw in relations between Syria and France after Sarkozy last year ordered a halt to diplomatic contacts with Damascus, which he blamed for stoking tensions in neighbouring Lebanon.
"The discussion comes in accordance with French pledges to reopen contact on the highest level with Syria, as soon as tangible progress was made towards the resolution of the Lebanese crisis," the statement said.
Syrian state media had earlier reported that Sarkozy had praised Damascus's efforts in helping end an 18-month crisis in Lebanon during a telephone call with Assad.
Sarkozy's office said the French president was pleased about recent contacts between Syria and Israel. The two countries said last week they had opened indirect talks mediated by Turkey, the first confirmation of any talks since 2000.
Syria dominated Lebanon until 2005 when the Beirut assassination of statesman Rafik al-Hariri triggered international pressure that forced Damascus to withdraw troops from its neighbour.
Damascus still wields substantial influence over politics in Lebanon through allies including Hezbollah and the Amal movement, and Paris had accused the Syrians of looking to promote political instability in Lebanon.
A deal mediated by Qatar this month ended the standoff between Lebanon's ruling coalition and an opposition alliance led by Hezbollah -- a group backed by both Damascus and Tehran.
Sarkozy, whose foreign minister failed last year to mediate an end to the crisis, "praised the intensive efforts made by (Assad) to make the Doha agreement succeed", Syrian news agency SANA reported.
France, Lebanon's former colonial power, backed the ruling coalition during the crisis, along with the United States and Arab countries including Saudi Arabia.
The Lebanon conflict turned violent this month and 81 people were killed. The bloodshed triggered the Qatari-led mediation.
The Doha agreement secured the opposition's demand for veto power in a new cabinet and paved the way for the election of army chief Michel Suleiman as president on Sunday. Lebanon had been without a president since November.