Mr Hollande warned that "separated, we run the risk of divisions, dissension and quarrels".
The two will hold talks later in Berlin amid a flurry of diplomatic activity in the wake of so-called "Brexit".
The pound fell further in early trading in Asia on Monday as markets reacted.
UK Chancellor George Osborne made a statement before the start of trading in the UK in a bid to calm markets.
He said the UK was ready to face the future "from a position of strength", although he accepted the economy would have to confront challenges and that further volatility on financial markets was likely.
Mr Osborne said that thorough contingency plans were in place, in discussion with the Bank of England, and that "we are equipped for whatever happens". He indicated that there would be no immediate emergency budget.
In other developments:
British Prime Minister David Cameron will hold a cabinet meeting on Monday
Boris Johnson, who led the Leave campaign and is tipped to replace Mr Cameron, has said the UK will continue to "intensify" co-operation with the EU
Embattled UK opposition Labour leader Jeremy Corbyn says he will stand in any new party leadership election amid calls for his resignation in light of the referendum result. Three more shadow ministers quit on Monday
Speaking on Sunday, Mr Hollande said there was no going back on the UK's decision, adding: "What was once unthinkable has become irreversible."
Her priority is to get Britain out smoothly as soon as is practical and to safeguard the future of the EU.
The meeting is as much about image as content, says the BBC's Europe editor Katya Adler - a signal and a photo op ahead of Tuesday's summit of all EU leaders that the EU is united in purpose and unflustered by the British vote.
US Secretary of State John Kerry is also due in London and Brussels for talks.
Speaking in Rome on Sunday, Mr Kerry expressed regret at the UK's decision but said the US would maintain close ties with the EU.
"Brexit and the changes that are now being thought through have to be thought through in the context of the interests and values that bind us together with the EU," he said.
US President Barack Obama has already said that the special relationship between the US and the UK would endure despite Britain's decision.
Over the weekend, European Commission President Jean-Claude Juncker said the process for Britain's withdrawal from the bloc should begin "immediately".
Several EU foreign ministers also urged Britain to start the process soon.
However, Foreign Secretary Philip Hammond indicated the UK would resist pressure for a swift start to negotiations, insisting that "nothing is going to happen at the moment".
That position was supported by Chancellor Merkel's chief of staff, who said Britain's politicians should take time to review the consequences of leaving the EU.
"Politicians in London should take the time to reconsider the consequences of the Brexit decision - but by that I emphatically do not mean Brexit itself," Peter Altmaier said.
David Cameron has said he will step down by October, allowing his successor to conduct the exit talks and, presumably, trigger Article 50 of the Treaty of Lisbon, which sets a two-year deadline for an exit deal.
Mr Osborne said on Monday the UK should only trigger Article 50 when it was ready to do so.
Last Thursday's referendum result has shaken the European Union but also exposed deep divisions within the UK itself.
Britain as a whole voted by 52% to 48% to leave but in Scotland the picture was different, with 62% backing remain.
Scotland's First Minister Nicola Sturgeon has told the BBC that the Scottish parliament could try to block the UK's exit from the EU.
She said that she and her colleagues would begin talks with Brussels officials about Scotland possibly remaining in the EU.
On Friday, Ms Sturgeon confirmed that a second Scottish independence referendum was back on the table.