The pair will discuss how to counter terrorism, and take the fight against the Islamic State (IS) in Syria and Iraq, UK officials said.
Mr Cameron hailed a universally approved UN Security Council resolution to “redouble” action against IS.
The IS claimed responsibility for the recent Paris attacks.
Mr Hollande will meet Russian President Vladimir Putin, German Chancellor Angela Merkel and US President Barack Obama.
A French-drafted UN document asking countries to “combat by all means this unprecedented threat” has been approved, therefore the world must now take note.
BBC’s UN correspondent Nick Bryant said.
However France – which is already carrying out air strikes against Islamic State in Syria – argues that military action is legally justifiable because of the right of countries to defend themselves, he added.
Mr Cameron said the UN vote was an important moment which “shows beyond doubt the breadth of international support” to “eradicate” IS.
On Saturday, a Russian Foreign Ministry official stated the country was ready to discuss UK involvement in air strikes in Syria.
Mariya Zakharova told state television news programme Vesti: “Our position is absolutely clear: there should be co-operation, so that any (actions) are not targeted at destroying the Syrian state.”
Russia and the UK have in past shared different views on how to solve Syria’s long-running civil war.
Two years ago, MPs voted against possible UK military action against President Bashar al-Assad’s government in Syria.
Parliament however later approved British participation in air strikes against IS extremists in Iraq.
On Saturday, Labour leader Jeremy Corbyn said his party would support “every necessary measure” to protect people in the UK, but warned people “must not keep making the same mistakes” when responding to acts of terror.
It was “vital” during a time of tragedy “not to be drawn into responses that feed a cycle of violence and hate”, he said.
Defence Select Committee chairman, Conservative MP Julian Lewis, said he was “standing firm in his belief that air strikes were not the answer.”
“I am in favour of effective military action to destroy Daesh, Isil, (but) bombing alone, without credible ground forces, is ineffective action,” he told the BBC.
“There is little, if any, evidence in history of a successful bombing campaign unless there were ground forces to take over.”
The SNP said “the prime minister should not take the UN resolution as an authorisation for UK military action.”