Conditions for peace
Hostility between Israel and Syria is one of the problems underlying efforts to seek a broader Middle East peace settlement.
Syria has repeatedly demanded the return of the strategic Golan Heights, which Israeli captured in the 1967 war and unilaterally annexed in 1981, as a non-negotiable condition for peace.
Meanwhile Israel accuses Syria of backing armed groups such as Hezbollah and Hamas.
This week al-Assad told a meeting of Arab politicians that Syria would not "put forward conditions on making peace" but warned it had "rights that we will not renounce," the SANA news agency reported.
Earlier on Friday, al-Assad hailed a "climate of trust" with France, welcoming a "resumption of good relations" between the two countries.
Our correspondent said it comes after Sarkozy reached out to the Syrians a year ago.
"Remember they had a dreadful relationship when Jacques Chirac was president. Sarkozy said he was going to sort that out," Fisher reported.
But the Syrian leader said his country had not "yet reached a revival of trust between Syria and the United States," and called on Barack Obama, the US president, to do more for the stalled Middle East peace process.
"What president Obama said about peace was a good thing. We agree with him on the principles, but... what is the plan of action? The [peace process] sponsor must come up with a plan of action," al-Assad told Le Figaro.
"The weak point - it's the American sponsor."
The Syrian president also repeated his position that Damascus must review a partnership agreement with the European Union, which had been due to be signed in October, calling on the bloc to have "more political independence".
"The Europeans have turned completely towards the United States, to Syria's detriment. A partner must be a friend and we haven't noticed that from Europe these last years," he said.
Damascus and the EU first drew up the draft partnership pact in 2004, but it was never signed by European countries, amid concerns by some nations of human rights abuses in Syria.