He spoke after it emerged that the suspected Belgian ringleader of the attacks had entered France undetected.
Belgian PM Charles Michel has defended Belgium’s security services amid claims the attacks were organised there.
It comes as EU interior and justice ministers are to hold emergency talks.
The meeting in Brussels is expected to discuss tightening checks at the external borders of the EU’s passport-free Schengen area.
Key questions remain after attacks
On Thursday, French prosecutors confirmed that Islamic State (IS) militant Abdelhamid Abaaoud was among those killed in a police raid the previous day.
His bullet-riddled body was found in the wreckage of a flat in the Paris suburb of Saint-Denis.
Investigators had identified him as the most likely organiser of last Friday’s attacks, but it was initially thought he was in Syria.
At a news conference, Mr Cazeneuve said “no information” had been received from other European countries about his arrival on the continent.
But he said he had received intelligence that Abaaoud had passed through Greece on his return from Syria.
“It is urgent that Europe wakes up, organises itself and defends itself against the terrorist threat,” Mr Cazeneuve told reporters.
French Prime Minister Manuel Valls said some of those involved in the attacks had taken advantage of the migration crisis in Europe – which has seen thousands of asylum seekers arrive on the continent – to “slip into” France unnoticed.
One of the attackers, who blew himself up outside the Stade de France, has been traced by his fingerprints to Greece where he was registered as a migrant.
A draft resolution for Friday’s EU meeting says ministers will agree to implement “necessary systematic and co-ordinated checks at external borders, including on individuals enjoying the right of free movement”.
Correspondents say Belgium has found itself under pressure after the attacks. French President Francois Hollande said they were “planned in Syria, prepared and organised in Belgium”.
A former senior French intelligence official has also been quoted in French media as saying that “the Belgians just aren’t up to it”.
In an address to parliament on Thursday, Belgian Prime Minister Charles Michel said it was intelligence from his country’s security services that had led to the huge raid in Saint-Denis.
“I do not accept the criticisms which were aimed at denigrating the work of our security services,” he said.
Mr Michel unveiled new security measures including jailing jihadists returning from Syria and extending detention periods for terror suspects.
Abaaoud grew up in the Molenbeek district of Brussels which has been described as a hotbed of extremism.
Suicide bomber Brahim Abdesalam, who attacked a cafe in Paris, and his brother Salah, who is on the run following the attacks, are also from Molenbeek.
On Thursday, the French Parliament extended a state of emergency for a further three months from 26 November.
Eight people were arrested following the raid in Saint-Denis. A woman at the flat – reported in French media to be Abaaoud’s cousin – died after detonating a suicide vest.
What is Islamic State?
IS is a notoriously violent Islamist group which controls large parts of Syria and Iraq. It has declared its territory a caliphate – a state governed in accordance with Islamic law – under its leader Abu Bakr al-Baghdadi.
What does it want?
IS demands allegiance from all Muslims, rejects national borders and seeks to expand its territory. It follows its own extreme version of Sunni Islam and regards non-believers as deserving of death.
How strong is IS?
IS projects a powerful image, partly through propaganda and sheer brutality, and is the world’s richest insurgent group. It has about 30,000 fighters but is facing daily bombing by a US-led multi-national coalition, which has vowed to destroy it.