Paris and Berlin are racing to bridge the gap between Macron's ambitious EU reform agenda and Chancellor Angela Merkel's more prudent approach by a crunch eurozone summit on June 29th.
French Finance Minister Bruno Le Maire spent nearly 14 hours holed up with his German counterpart Olaf Scholz at a Paris hotel on Saturday, the source told AFP.
While the talks, which lasted into the early hours of Sunday, did not yield an agreement the ministers discussed "all the unresolved issues" and made "substantial progress", the source said.
"We still have work to do before agreeing on a roadmap," the source continued, adding "there is agreement on nothing until there is agreement on everything" and that Le Maire and Scholz planned further talks in the coming week.
Macron is on a drive to reconcile Europeans with the European Union after years of austerity and mass migrant flows have fuelled the rise of populist and nationalist parties.
He has seized on Britain's vote to leave the bloc as a chance for closer integration, with the aim of adopting sweeping changes before European elections in May 2019.
But Germany and other northern European states have baulked at his calls to give the eurozone its own big "rainy day" fund, fearing the more fiscally prudent north will have to pick up the tab for overspending by the more profligate south.
In an interview last weekend, days after a eurosceptic government took office in Italy, Merkel made some concessions.
She said the eurozone's top economy would support Macron's call for an investment fund to help poorer European countries catch up in the areas of science, technology and innovation.
But the size of the fund remains a major bone of contention, with Merkel saying it should be "at the lower end of the double-digit billions of euros range" while Macron has called for a budget amounting to "the equivalent of several points of the GDP of the eurozone".
Merkel also detailed her proposals to upgrade the eurozone's bailout fund into a European Monetary Fund -- under strict lending conditions and on condition that member states retain oversight over the body.
Macron's office welcomed the concessions but during a visit to Berlin on Friday Le Maire called on Germany "to go further".
"It is a courageous response that goes in the right direction," Le Maire told AFP.
"Is it sufficient? No. We think you have to go further and that this is a unique, historic opportunity to make very significant progress toward better integration of the eurozone," he said.
By Etienne Balmer and Clare Byrne