"This is not a Greek exit from the eurozone," he told reporters following a meeting of eurozone ministers.
"The 18 countries, apart from Greece, all said clearly that Greece was in the euro and should remain in the euro whatever the difficulties of the moment," he added.
"France is available at any time to resume dialogue with Greece ... we are available today, tomorrow, the day after tomorrow ... to try to find a solution that is solid and stable for Greece," Sapin said.
On Saturday, eurozone finance ministers meeting in Brussels rejected Greece's request to extend its existing bailout program past a Tuesday, June 30, deadline.
Greece wanted the extension so it could hold a national referendum on July 5 to let voters decide whether the country should accept the austerity terms that the government of Prime Minister Alexis Tsipras bitterly opposes.
Then, early on Sunday morning, the Greek parliament voted to move forward with the referendum, after a day on which many Greeks lined up at cash machines to withdraw money from banks out of concern that a fresh financial crisis could be at hand.