The entry into force on Saturday of the July 14 deal between Iran and world powers "is a good thing... But we should be extremely strict in monitoring its implementation," he said.
"We will be very vigilant," he told reporters on the sidelines of the World Future Energy Summit in Abu Dhabi.
The International Atomic Energy Agency confirmed late Saturday that Tehran had complied with its obligations under the accord, leading the United States and the European Union to lift sanctions imposed over Iran's disputed nuclear programme that had crippled its economy for a decade.
Fabius said he hoped "the state of mind that allowed for this deal will have positive consequences on Iran's general attitude in the region".
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Peace talks scheduled to take place in Geneva on January 25 to resolve Syria's deadly conflict would provide the "first opportunity" to test Tehran's intentions, he said.
Iran -- alongside Russia -- is a key backer of Syrian President Bashar al-Assad's regime, which has been locked in deadly fighting with opponents since an uprising erupted in 2011.
Saudi Arabia severed its diplomatic ties with Iran earlier this month after protesters attacked its missions in the Shiite-dominated Islamic republic.
The protests erupted in response to the execution in the Sunni-ruled kingdom of prominent Shiite cleric Nimr al-Nimr.
Asked if France could play a mediator role between Riyadh and Tehran, Fabius said: "Mediation is not the right word, but we are talking to both sides."
Fabius said he would meet Saudi King Salman tomorrow ahead of a meeting on economic cooperation between France and Saudi Arabia in March.