Belgium raised its anti-terror alert to its highest level and security was also stepped up at Germany's Frankfurt airport.
French Prime Minister Manuel Valls, Interior Minister Bernard Cazeneuve and Defence Minister Jean-Yves Le Drian rushed to an emergency meeting in Paris.
The Gare du Nord stations closed briefly and the direct train to Brussels was to stop at Lille in northern France.
Salah Abdeslam is being held in Brussels and questioned about his role in November's Paris attacks and investigators reported on Monday that he had been planning new attacks and had a number of accomplices, some still at large.
Earlier shots rang out and cries in Arabic are reported to have been heard before two explosions shook the airport, causing at least 13 deaths and 35 injuries, according to VRT television, which said they were the work of suicide bombers.
Shortly afterwards an explosion went off at Maalbeck metro station, in the area where European Union offices and institutions are situated.EU staff were told to stay at home.
Many injuries were reported there but no deaths.
The Belgian cabinet held an emergency meeting on hearing the news.
To read our coverage of the November Paris attacks and their aftermath click here