Eurostar told travelers to travel only from Paris to London "if absolutely necessary".
Its services have been hit by serious delays because long lines have been formed due to the industrial action of French customs officials.
Four trains were canceled on Sunday, and three more on Monday.
The company says tickets can be changed for free, or refunds can be requested.
"We recommend that you do not travel, unless absolutely necessary," Eurostar advised on its website.
Customs officers demand higher salaries and better working conditions.
They also want more staff that they say will be needed after Brekit, to help prosecute British citizens who will no longer have passports of the European Union.
Industrial action should last until March 19th.
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Travelers are complaining about social media about long ranks in Paris.
Catherine Hope tweeted that she took four and a half hours to clear all the rows.
The other passenger said they were waiting for two and a half hours.
Eurostar says the delays are on average two hours and expect similar delays on Monday.
Last week, French trade unions, representing around 17,000 clients, rejected the government's offer to raise the salary of 14 million euros, saying it was not enough.