Some people have been waiting up to three hours to clear passport controls, with freight traffic building up on roads approaching the Kent port.
A Port of Dover spokesman advised customers to allow plenty of time for their journey.
France has been under a state of emergency since last November.
The country's National Assembly voted to extend the measure by six months in response to last week's attack in Nice in which 84 people were killed and scores injured when a lorry was driven into crowds.
The state of emergency was brought in after terror attacks in Paris on 13 November that left 130 people dead.
Latest updates on the Port of Dover and other Kent stories
A P&O Ferries spokesperson said: "We are doing everything we can to allow passengers to begin their journey as quickly as possible.
"If passengers miss their allocated ferry they will be able to board the next available ferry at no additional cost."
Disgruntled travellers have taken to Twitter to express their dismay.
John Hippisley said "terrible PR for the French Authorities I appreciate the need to protect the border but clearly all tourist not terrorists".
The extra security checks have been causing delays since the early hours.
DFDS Seaways advised customers on Twitter at 13:00 BST that they should "allow 180 minutes to complete the check-in process... the port is very busy".

Westminster Council has objected to plans for 128 new boxes since January, including 80 from Maximus Networks Ltd.
Birmingham and Manchester councils say that the boxes are effectively little more than advertising boards.
They say they cannot stop them as planning permission is not needed, just an Ofcom licence.
Maximus Networks said it was offering "a truly useful" public service.
Three cities have had 301 applications for new phone boxes in 12 months - 158 in Westminster, 104 in Birmingham and 39 in Manchester.
Councils can object to Ofcom's approval of the boxes but only on two grounds: location and design.
A Department for Communities and Local Government spokesman said it was considering the matters raised by councils.
Each Maximus Networks box would provide 1.3m x 2m of advertising space which does not need local authority consent.
Westminster Council said the boxes, which the company planned to install on Oxford Street, Victoria Street and Baker Street, would offer no wi-fi or internet connectivity.
"This scheme will create ugly and unwanted advertising space," Councillor Richard Beddoe said.
However, Maximus founder Ashley Smatt said: "We believe what we have planned will be the envy of the world.
"There are currently around 66,000 calls a week from phone boxes across the UK and we believe there is a demand for this."
Councillor Daniel Astaire, of Westminster Council which rejected another operator's proposal for 48 boxes on Tuesday, said companies "are trying to make a quick buck" with "ugly hoardings on some of our most iconic streets".
Birmingham City Council deputy leader Ian Ward said "open access wi-fi and widespread mobile phone use" made the kiosks "redundant".
But he said he anticipated more coming, "because city centres offer a highly lucrative market for advertising and there's no restriction on how many can be installed".
Ofcom said it had no evidence Maximus had breached any obligations but it would "be concerned" if permission was "used to provide advertising space under the cover of a largely unwanted public call box service."
Councillor Pat Karney, of Manchester City Council, said the only people he had seen using phone boxes "are drug dealers, particularly around the Piccadilly Gardens area".
Redundant kiosks are increasingly being put to inventive uses, from defibrillator storage to miniature art galleries.
There are about 46,000 remaining public kiosks across the UK including about 8,000 traditional red ones.
About 2,500 of those in England are listed, according to Historic England.
Thousands of Cross-Channel ferry passengers are facing long delays at the Port of Dover amid heightened French security checks.
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Councils are fighting plans for hundreds of new "ugly and unwanted" phone boxes while they seek a change in the law.