Dr Antony McRoy, a Christian author on radical Islam, told Premier migrants who refuse to give their identities should not be allowed into the continent.
It is claimed one of the attackers that targeted Paris on Friday night had masqueraded as a Syrian refugee in order to enter Europe from Greece.
"It was inevitable that IS or al-Qaeda would take advantage of this [the refugee crisis]," Dr McRoy said on the News Hour.
He said about 30% of the migrants coming to Europe had refused to be documented in fear of being deported.
"Obviously that is not something we can allow in light of Paris, there must be clear documentation of everyone who has entered Europe's borders.
"Anyone who refuses to be documented must be immediately arrested and deported," he added.
Europe's agreement of free movement between countries had "made it possible" for terrorist to attack Europe, Dr McRoy claimed.
Meanwhile the suspected mastermind of the Paris attacks has been identified, as authorities mounted a massive security operation amid growing questions about how the terrorists evaded detection.
Belgian Abdelhamid Abaaoud has been singled out as a key figure in the plot that saw 129 people murdered in coordinated strikes in the French capital on Friday.
He is believed to be linked to thwarted attacks on a Paris-bound high-speed train and a church in the Paris area, an official said.
It came as Interior Minister Bernard Cazeneuve revealed that 168 locations across France were raided overnight, with 104 people placed under house arrest in the past 48 hours.
Several more individuals have been detained, while officers have seized dozens of weapons including a Kalashnikov assault rifle and automatic pistols.
"This is just the beginning. These actions will continue.
"The reply of the republic will be solid and total. Those who want to hurt the republic, they will be attacked, they will be dealt with, and who helped them," Mr Cazeneuve said.
A minute's silence was observed in tribute to the victims of the massacre on Monday.
Fr Aidan Troy, a priest at St Joseph's Church in Paris, told Premier Paris was "much more normal today with people back at work".
"But I would still say its tense, that's my impression. I was in a school this morning and the parents are terribly worried about their children but they have to come out," he added.
It was revealed that one of the suicide bombers who blew himself up in the Bataclan music hall had featured in a previous terrorism investigation, but slipped through the net.
Officials identified the assailant as Samy Amimour, a 28-year-old Frenchman, who had been charged in a terror probe in 2012.
He was placed under judicial supervision but dropped off the radar - prompting authorities to issue an international arrest warrant.
An attacker who blew himself up outside the national soccer stadium was found with a Syrian passport in the name of Ahmad Al Mohammad, a 25-year-old born in Idlib, a city in the north-west of the war-ravaged country.
His fingerprints matched those of someone who passed through Greece in October.
In another development, claims emerged that Turkish authorities flagged one of the attackers to their French counterparts last year, but received no response until after Friday's assault.
An official was reported to have said that Omar Ismail Mostefai was identified as a possible "terror suspect" in October 2014, with French authorities said to have been alerted in December 2014 and in June 2015.
A huge security operation continues in the Brussels suburb of Molenbeek as police hunt for Salah Abdeslam, 26, who rented a car used to carry gunmen to the Bataclan.
French authorities missed an opportunity to detain him when he was questioned and released just hours after the carnage in Paris. Abdeslam is one of three brothers linked to the atrocity.
Dr Antony McRoy speaking to Premier's Antony Bushfield:
