French rail company SNCF says its high-speed network has been targeted by "malicious acts" aimed at paralysing the system.
It comes hours before the opening ceremony for the Paris Olympic Games.
Several high-speed TGV lines have been hit to the west, north and east of Paris and queues have formed at Gare Montparnasse station in the city.
A number of trains have been cancelled and SNCF has warned that the situation could last "at least all weekend while repairs are conducted".
Eurostar services in France to and from Paris are being diverted and several trains have been delayed, the rail firm says in a statement.
The high speed line between Paris and Lille has been affected while journey times have increased by 90 minutes following "co-ordinated acts of malice in France", it says.
Several trains have been cancelled, it adds.
Trains between Paris and London are still running on "classic" lines but passengers can expect journey times to be an hour longer.
The president of the SNCF group told French news outlet BFMTV that 800,000 customers have been affected.
