The theft near Lille, which French media says is of around 600 metres of copper cables, is causing trains to be rerouted, leading to extended journey times.
Routes to and from London are subject to last-minute cancellations and severe delays, Eurostar said.
It added that impacted passengers can change their travel plans for free or request a full refund.
“We’re very sorry for the impact this is having on our customers,” Eurostar said in a statement.
“Our teams are working closely with the French authorities and infrastructure teams to manage the situation and restore services safely.”
The operator says one track has reopened, allowing some trains to run in both directions until full repairs are completed.
Water is being handed out to passengers onboard delayed trains, and stations are also very busy.
The railway line in France was closed for much of the afternoon and evening on Tuesday after the two fatalities between Lille and Paris.
Services were cancelled on routes to and from Paris while trains between London, Brussels and Amsterdam ran with delays.
Eurostar said disruption continued into Wednesday as trains and crew were displaced.