Mr Macron's comments came as diplomats sought an agreement between Iran and the US to return to compliance with their 2015 nuclear pact with world powers.
The European Union circulated a draft text last month on which the Iranians and Americans have both sent written comments.
The EU's foreign policy chief Josep Borrell on Wednesday said there was common ground between the sides but urged diplomats not to "lose this momentum".
In an aside during a speech to French ambassadors on Thursday, Mr Macron said: "I hope that in the next few days the JCPOA [Joint Comprehensive Plan of Action] will be concluded."
France, Britain, Germany, Russia, China, the US and the EU signed the pact with Iran in 2015, offering sanctions relief in exchange for limits on Tehran's nuclear activities.
Those limits, including a maximum level of uranium enrichment and curbs on Iranian centrifuges, were meant to prevent the country from acquiring a nuclear weapon.
The US under former president Donald Trump abandoned the deal and restored sanctions in 2018, prompting Iran to openly flout the limits under the JCPOA.
Joe Biden's administration entered talks last year to revive the agreement and a deal has appeared close for months.
The talks in Vienna were postponed in March, as Russia's presence added a fresh complication after the invasion of Ukraine, but the process was revived by the EU's draft proposal in July.
"I got feedback from all delegations. I got comments from Iran and the United States, which I both found reasonable," Mr Borrell said on the sidelines of an EU foreign ministers' meeting.
"To me, it is clear that there is a common ground, that we have an agreement that takes into account, I think, everyone's concerns. I am hoping that in the coming days, we are not going to lose this momentum and we can close the deal."
Mr Borrell did not say how the proposals differed, but Iran has sought to use the talks to bring an end to separate inquiries by the International Atomic Energy Agency into undeclared nuclear sites.
Washington said the two issues were separate and that a revived JCPOA would not free Iran from its obligations under nuclear non-proliferation treaties.