The fatal accident took place at about 6.00pm on Friday at Sainte-Marie-Cappel, about 50 km south-east of Calais, firefighters said.
Sources told French media that the death appeared to be a suicide.
The London-Paris train continued to the French capital but the company announced that there would be delays of two to two and a half hours of seven or eight Paris-London trains and six London-Paris ones.
High-speed TGV trains between the north-eastern city of Lille and the Channel ports of Dunkirk and Calais were diverted, leading to delays of 40 minutes to an hour, according to Europe 1 radio.
Friday is a busy day for Eurostar, with the number of passengers rising ahead of the weekend.