Eurostar is urging passengers to avoid travelling until after Wednesday unless their journey is “absolutely necessary”.
The cross-Channel rail operator warned that industrial action by French customs workers will continue to cause delays and long queues over the coming days.
Passengers were forced to queue for more than five hours over the weekend.
On Monday, Eurostar cancelled three trains and several others were delayed due to the industrial action.
French customs officials are demanding more pay and resources ahead of Brexit.
They have been working to rule by carrying out more stringent checks than normal in an attempt to demonstrate the impact of tighter border controls after the UK withdraws from the EU.
This caused long queues at the port and Eurotunnel terminal in Calais, northern France last week.
Eurostar said in a statement: “French customs officers at Paris Gare du Nord continue to take part in industrial action.
“As a result, the regular pre-departure security checks are taking longer than usual and this is causing delays on departure in Paris.
“We are very sorry for the inconvenience this is causing passengers, and to provide as much flexibility as possible we are offering a free exchange or refund to any passenger who would prefer to postpone their trip.”