He said both leaders had authorised him to make the announcement. It would be the first time the two countries had full-fledged embassies in each other's countries since Lebanon became independent in 1943 and Syria in 1945.
Sarkozy is also scheduled to visit Syria by mid-September in an effort to build relations between Paris and Damascus. Relations between the two countries have been tense since the assassination of Rafiq al-Hariri, a former Lebanese prime minister, in 2005, which France believes was orchestrated from Damascus.
France and the US have previously called on Lebanon and Syria to establish full diplomatic relations after Damascus pulled its troops out of Lebanon in 2005, ending nearly three decades of military presence.
Al-Assad was welcomed in Paris for a meeting at the Elysee palace before joining 40 other foreign leaders.
The Syrian president is among 43 leaders who will launch a so-called Union for the Mediterranean at a summit in Paris on Sunday.
Al Jazeera's Jacky Rowland, speaking in the French capital, said al-Assad is soaking up the international exposure from this trip.
She said: "The Syrian president's willingness to build ties with Lebanon, which have been strained for so long, is music to French ears.
"This is also something that Sarkozy will take credit for, and essentially see this as a diplomatic breakthrough."
Al-Assad met Michel Sleiman, the Lebanese president, the first time since he was elected in May, ending Lebanon's worst political crisis since the 1975-1990 civil war.
Sheikh Hamad bin Khalifa Al Thani, Qatar's emir, whose country brokered the power-sharing deal that ended the country's crisis, also met the two leaders.
However, a meeting between al-Assad and Ehud Olmert, Israel's prime minister, has been ruled out.
Sarkozy also raised human rights issues during his one-on-one talks with Assad on Saturday and try to advance the Israeli-Syrian peace process, aides said.
Despite concerns over Syria's rights record, France sees Assad's willingness to take part in the new Mediterranean forum and its indirect talks with Israel as signs that Damascus is seeking a more constructive role in the Middle East.
While the US continues to view Syria as a "terror state", France under Sarkozy has moved to renew high-level ties that suffered as a result of the 2005 assassination of al-Hariri, Lebanese ex-premier, who was a personal friend of Jacques Chirac, the former French president.
Israel and Syria, which technically remain at war since the creation of the Jewish state in 1948, have held three rounds of indirect talks through Turkey since March, raising peace prospects after an eight-year break.
Sarkozy has invited leaders from 44 countries, including Arab nations and Israel, for the founding summit of the union aimed at boosting co-operation between EU and bordering Mediterranean states.
On Monday, the Syrian leader will join about a dozen leaders to watch the annual Bastille Day military parade on the Champs Elysees during France's national celebrations.
However France's Bernard Kouchner, the foreign minister, last month commented that he was "not particularly pleased" by al-Assad's presence at the July 14 national fete.
While al-Assad will be applauding troops marching in the Bastille Day parade, Chirac will be conspicuous by his absence.
Officials have denied the former president's decision to stay away was linked to al-Assad.
Al-Assad's visit comes during France's presidency of the 27-nation European Union.