While acknowledging the Greeks' right to determine their own future, Hollande told Greek Mega Channel television that if it appears from the vote that they doesn't want to respect the bailout deal "there will be countries in the eurozone which would prefer to end Greece's presence in the eurozone."
Greece holds its second parliamentary election in six weeks this Sunday, after a May vote failed to produce any workable majority. The leftist Syriza party, which has pledged to tear up the bailout deal, stands a good chance of winning, and even parties which backed the rescue now favour renegotiating its terms.
"I am in favour of Greece remaining in the eurozone, but Greeks should know that this requires there be a relationship of trust," Hollande said in a transcript of the interview provided by his office.
Hollande said he had lobbied his EU counterparts for bloc funds be speeded up so Greece, now in its fifth year of recession, can return to growth.
He pledged he would continue to push for their release and warned Greeks "the abandoning pure and simple of the (bailout and austerity) memorandum would be seen by many eurozone members as a break up."
Hollande, who has pushed for the eurozone to shift its focus from austerity to growth, said the situation has now evolved even further.
"The financial situation is such that we must also have guarantees so banks can be preserved and supported," said the French president.
"We are already in another stage," of the eurozone crisis. "This is what the Greeks must also understand," he added.
The European Commission pressed governments for urgent action on the eurozone crisis on Wednesday, seconding a German call for more integration and structural reforms.
EU leaders are growing international pressure to take bold action when they hold a summit on June 28 and 29 as the eurozone crisis increasingly threatens global growth prospects.
Analysts have called for steps towards fiscal and banking unions that would reduce concerns about the finances of weaker eurozone countries.