During a phone call with Iran President Hassan Rouhani, Macron expressed his "strong concern" about the consequences of abandoning the 2015 accord, the BBC reported on Saturday.
Rouhani called on European countries to act urgently to save the deal aimed at curbing Iran's nuclear programme.
The agreement has been in jeopardy since the US pulled out last year. US President Donald Trump later imposed punishing sanctions on Iran.
In May, Iran responded by stepping up production of enriched uranium, used to make reactor fuel but also potentially nuclear bombs.
Iran has already stockpiled more enriched uranium than the country was supposed to.
The country has been expected to announce on Sunday that it will breach another limit by taking the enrichment process to a higher level.
The French presidency published a statement (in French), saying that President Macron had spoken for more than an hour with his Iranian counterpart.
Macron said he was very concerned about the "risk of a further weakening" of the treaty and "the consequences that would necessarily follow".
The statement said the two leaders had agreed "to explore by July 15 the conditions for the resumption of dialogue between all parties" beyond a Sunday deadline announced by Iran.
Rouhani had previously given the five countries still party to the deal the UK, France, Germany, China and Russia until Sunday to meet their commitment to shield Iran from the sanctions' effects.
The French statement also said Macron would continue consultations with the Iranian side and international partners to reduce tensions.
President Rouhani urged the European signatories to act to save the deal. "Lifting all sanctions can be the beginning of a move between Iran and six major powers," he said.
( With inputs from IANS )