"France [...] is a point of contact and we will play this role of a point of contact to the last to make our contribution to a success that is indispensable for everybody," Sapin said on arrival at the Eurogroup meeting on Saturday afternoon.
France is reported to have played a major role in the drafting of Greek proposals that raised hopes of an agreement only to see them dampened by Germany and its north European allies, who declared that they did not trust the Syriza government to keep its promises.
The discussions would be "rigorous", Sapin said, "because confidence is a decisive element in the agreement, if we want to have a global agreement and a lasting agreement".
The European summit was cancelled on Sunday, European Council president Donald Tusk announced in a twee.
A finance ministers' meeting at 11.00am was to be followed at 4.00pm by a meeting of eurozone leaders that would last "until a decision is taken", he said.
Italian Prime Minister Matteo Renzi slammed Germany's tough stance in an interview published by Il Messaggero newspaper on Sunday.
"Italy does not want Greece to leave the eurozone and I'm telling Germany 'Enough is enough!'," he said. "Humiliating a European partner while Greece has given in on everything or nearly everything is unthinkable."
German Finance Minister Wolfgang Schaeuble on Saturday proposed that Germany should be temporarily suspended from the eurozone unless it offers more concessions, such as placing the fund that manages income from privatisation abroad so that the money is used exclusively to repay Greece's debt.
"What is going on is that they want to humiliate Greece and the Greek people or overturn [Prime Minister Alexis] Tsipras's government," was the reaction of Syriza member Dimitrios Papadimoulis, who is vice-president of the European parliament.
In France Jean-Luc Mélenchon's Left Party claimed that Germany does not want an agreement "but a complete Greek capitulation even at the price of a Grexit" and called on President François Hollande to "turn words into deeds and give his full support to Greece's proposals".
The leader of France's opposition Républicains party, Nicolas Sarkozy, was in Brussels for a meeting of the right-wing bloc in the European parliament.
The former president declared that Greece had "suspended itself from the eurozone" shortly before last weekend's referendum but this week said that "everything should be done to find a compromise".