"I am optimistic that we will have a good solution. We are not far from agreement," Le Maire said ahead of a meeting with Greek Prime Minister Alexis Tsipras.
"We are really doing our best to find an agreement," he had said earlier after seeing his Greek counterpart Euclid Tsakalotos.
"It's difficult. It's complicated," he said.
'Doing our best' on Greek debt relief deal, says France's Le Maire
At the June 15 meeting, Le Maire said he planned to propose a "mechanism" of "flexibility" to lessen Greek debt repayment based on its economic growth.
"It's a mechanism which should allow us to revise certain (debt) parameters based on Greek growth," he told reporters.
The issue of debt relief for Greece has sharply divided its international creditors, the European Union and the International Monetary Fund, for months in the latest round of talks.
The impasse has held up a tranche of bailout cash which Greece needs to repay loans in July, and Athens says its fragile recovery has also been impaired.
Tsipras has said he will ask EU leaders to resolve the issue at the end of June if no solution is forthcoming on Thursday.
"Piling drama on the problem helps no one," he said on Monday.
The Europeans expect Greece's economy to grow strongly and its government to bring in large surpluses in revenue in the coming years, allowing it to pay down its debts.
But the IMF is less optimistic, arguing there must be further relief for Athens before it can label its debt sustainable and justify loaning Greece any more cash.
New French President Emmanuel Macron last month called Tsipras after his election, saying he was in favour of "finding a deal soon to alleviate the weight of Greece's debt over time."
Macron's position puts him at odds with Germany where Greek debt relief -- following three different bailouts with public money for the country since 2010 -- is seen as a vote loser ahead of general elections in September.
Macron explained his thinking about Greece in an interview to the Mediapart website two days before his election.
"I am in principle in favour of a concerted restructuring of Greek debt and in keeping Greece in the eurozone. Why? Because the current system is unsustainable," he said