"Greece is in the eurozone. Greece has to stay in the eurozone," said Hollande following talks with German Chancellor Angela Merkel.
Merkel said the German position "since the beginning of the Greek programme" had been that Greece remain in the bloc and added that Berlin "would do everything to continue along this path."
"Today's Eurogroup (meeting of eurozone finance ministers) is the beginning of a phase of intensive work," said Merkel.
"There are still a lot of technical questions to solve, a lot of decision to be taken. I don't want to get into the details, it will be the finance ministers who will deal with the detail today," added the chancellor.
She called for an "improvement" in the Greek proposals, pointing out that the Bundestag lower house of parliament would next week vote on the Greece programme.
Hollande for his part said he knew of "no scenario today" that would lead to Greece being catapulted out of the bloc.
"We have the responsability to make sure that the commitments are respected and, at the same time, that the vote of the Greeks is heard," added Hollande.
The talks came as eurozone finance ministers were preparing to meet in Brussels Friday to consider a take-it-or-leave-it offer from Athens to extend its European loan programme.
The meeting will be the third in a little over a week as ministers battle to reach a compromise and prevent a damaging Greek exit from the single currency bloc.
Greece made the formal request for the loan extension on Thursday, offering concessions including a return -- if not in name -- of the hated "troika" of creditors that had audited the Greek economy during the bailout.
In substance, the two sides are not all that far apart, with new hard-left Greek Prime Minister Alexis Tsipras willing to press on with reforms, if different from those embraced by previous conservative governments.
In return, Tsipras wants the eurozone to agree to short-term funding to buy the time necessary to hammer out a new rescue deal.
With the European portion of the bailout soon to expire, Greece's creditors insist it needs extra financing to stave off default and a "Grexit" -- or Greek exit from the euro.