“My proposal still stands,” Calais mayor Natacha Bouchart told a press conference after the incident on Thursday. “We are sick of not being listened to.”
She called on the UK government to “send a message that migrants from Calais will not be welcomed”.
Bouchart, a member of the right-wing UMP party who first threatened to blockade the port after meeting Interior Minister Bernard Cazeneuve this week, also wants Britain to help pay for additional security measures, the UK border to be moved from Calais to Britain and British Prime Minister David Cameron to visit the town.
On Thursday about 85 migrants forced a gate and climbed over fences in an attempt to storm a ferry, about 15 reportedly later being found in lorries by police.
Ferries raised their ramps for about 15 minutes to prevent the migrants coming on board.
A second attempt by a crowd of about 150 failed.
The number of migrants in Calais has increased sharply in recent months, after declining over the last few years, and 1,000-1,400 are believed to be in and around the town.
Jean-Marc Puissesseau, the chairman of the local chamber of commerce, which manages the port, called for police to be permanently present so that they can immediately intervene if there are further attempts to storm the port.
“The migrants take more and more risks,” Maël Galisson of an umbrella group of aid organisations told the Voix du Nord newspaper. “Handling the question by exclusively police methods only adds to the problems and makes the situation worse.”
The Europe director and French representative of the UN High Commissioner for Refugees (UNHCR), which closed its Calais office in 2012 because of the decline, visited the town on Wednesday to meet Bouchart and other officials, as well as groups helping migrants.
Vincent Cochetel and Philippe Leclerc went to an illegal camp on the beach and attended a food handout.
A number would be given refugee status if they asked for asylum, UNHCR spokesperson William Spindler told the AFP news agency, adding that France has the responsibility to house those who wish to stay there but most do not want to do so.