The socialist French president is one of the few European leaders to have unabashedly thrown his support behind young leftist Prime Minister Alexis Tsipras during months of fraught talks with its EU and IMF creditor earlier this year.
"France must continue to stand by Greece," Hollande said after signing a strategic partnership with Tsipras offering French economic management expertise, especially to tackle tax evasion.
On his first visit to Athens since 2013, Hollande praised Greece's determination to stay the course of economic reform, which had put an end to talk of a 'Grexit' -- a Greek exit from the eurozone.
Now the debate is focused on a possible British exit from the EU -- or Brexit -- that would occupy European leaders in December, he said, saying it was a "serious hypothesis" that could not be ignored.
He also promised to support Greece as it grapples with a rising number of refugees landing on its shores.
"Greece is our frontier," Hollande said, pledging 60 French experts to help EU border agency Frontex staff emergency registration centres across the region.
"We must cooperate to protect our borders," he added, saying those who did not meet refugee criteria "should be turned back".
Earlier on Friday, the International Organisation for Migration said a record 48,000 migrants and refugees had landed on Greek shores over the past five days.
Hollande also addressed the Greek parliament, becoming the third French leader to do so after General Charles de Gaulle in 1963 and Nicolas Sarkozy in 2008.
When he arrived on Thursday, Hollande recalled the "bold decisions" taken by Tsipras, who in July agreed to more public spending cuts in return for a three-year, 86-billion-euro ($96-billion) EU bailout to prevent Greece crashing out of the eurozone.
"We did everything, France and Greece... for Greece to remain in Europe," he said.
Tsipras on Friday acknowledged that Hollande "was among those who persuaded me that I had to accept" the bailout.
Later, while visiting Athens University, Hollande said that during July's marathon talks, he had closely watched the leaders of countries that had recently joined the eurozone, thinking "who would be next for missing a target, for having a higher-than-forecast debt?"
The French leader has also pleaded for a renegotiation via an interest deferral of the soaring Greek public debt, which is equal to around 200 percent of the country's entire annual economic output.
Greece is undergoing a review by EU-IMF auditors after pushing through parliament another round of unpopular tax measures.
- 'Extreme' neo-liberal measures -
After a dispute on home foreclosures arose with the creditors, Tsipras on Friday lashed out at "absurd and extreme neo-liberal interventions" that threatened to undermine the bailout agreement.
"Such interventions threaten social peace... Greece signed a deal that it will honour. It did not sign a pact to surrender its sovereignty and destroy its social cohesion," the Greek leader said.
Hollande said he supported a Greek request to the European Union for a credit extension of 330 million euros ($363 million) in 2016 to cope with the influx of migrants following the arrival of more than half a million people since January.
"Centres must be created in Turkey so that people will not get as far as Greece, where we will not be able to receive them," he said.
Hollande also pledged to encourage French investment in Greece.