A joint Franco-Syrian statement issued after Assad met President Nicolas Sarkozy also said the French leader welcomed the Syrian president's strong determination to establish diplomatic relations with Lebanon.
Syria launched indirect peace talks with Israel this year under Turkish mediation but has insisted that it wants the United States to be the main broker in negotiations over the return of the Golan Heights captured by Israel in 1967.
The last talks direct between the Israel and Syria under US sponsorship broke down eight years ago and Washington has been reluctant to re-engage with Damascus because of its role in Lebanon and close ties with Iran.
The statement said Sarkozy would visit Syria by mid-September to relaunch relations between Paris and Damascus, which have been tense since the assassination of former Lebanese Prime Minister Rafik Hariri in 2005, which France believes was orchestrated from Damascus.
It also said the French leader, as current holder of the European Union's rotating presidency, would start the procedure to sign a long-stalled association agreement between Syria and the EU and its ratification, which were put on ice after Hariri's murder.
'Iran not seeking nuclear weapons'
Assad said following the meeting that Iran is not seeking to obtain nuclear weapons. Speaking at a press conference, Assad said Tehran had "no intention to possess nuclear weapons."
The French president called on Syria to use its relations with Iran to help end the stand-off over Tehran's suspected nuclear weapons drive.
"For France, the detention of nuclear weapons by Iran is not envisageable... President Bashar Assad bases himself on the declaration by the Iranian authorities that they are not seeking access to such weapons.
"So we ask Syria to convince Iran to provide proof, not just intentions, but proof", Sarkozy said.
The French and Syrian leaders were addressing a joint press conference at the Elysee palace, alongside Lebeanse President Michel Sleiman and Qatar's emir Sheikh Hamad bin Khalifa al-Thani.
Assad, who is among 43 leaders who will launch a new Union for the Mediterranean at a summit in Paris on Sunday, is marking the end of years of isolation in the landmark visit to France.
Paris meeting (Photo: AP)
Sarkozy also said Syria and Lebanon would open embassies in each other's countries.
The nations have not had full-fledged embassies in each other's countries since Lebanon became independent in 1943 and Syria in 1945.
Assad said last month that establishing diplomatic ties with Lebanon would be possible if a national unity Cabinet was formed in Beirut.
Such a government, including members of Syria's ally Hizbullah, was formed Friday after weeks of haggling.
Earlier, Lebanon's president says he wants to establish diplomatic ties with Syria and to visit Damascus.
Suleiman says Lebanon "wants an exchange of ambassadors and diplomatic relations with Syria."
He says he is satisfied with relations with Syria and that a visit to the country is "still on the agenda."
AP, Reuters and AFP contributed to this report