The agreement came after the G7 leaders discussed the issue at a summit in south-western France on Saturday evening.
The source said the priority remained to prevent Iran from obtaining nuclear weapons and defuse tensions in the Persian Gulf.
“As president of the G7, the president did indeed get the power to discuss and send a message to Iranian authorities on the basis of the exchanges we had last night,” the French official said, without providing any details.
The G7 summit was held a day after Macron held “constructive” talks with Iranian Foreign Minister Mohammad Javad Zarif in Paris.
Speaking to reporters on Friday, Zarif said the French president’s offers to save the JCPOA and Iran’s proposals were discussed in the meeting.
According to Zarif, the talks were in line with earlier phone conversations between Macron and his Iranian counterpart Hassan Rouhani.
He had also said that Macron would use the Saturday G7 meeting with world powers as an opportunity to discuss the offers.
Unconfirmed reports say the French president has shared his offer with US President Donald Trump on the sidelines of the G7 summit, asking him to let Iran sell its crude oil for a while in exchange for Iran’s return to its commitments under the 2015 nuclear deal, which the US withdrew from in 2018.