PARIS — A French rail strike has seriously disrupted train service around the country, cancelling a slew of train routes and snarling commutes for hundreds of thousands in Paris and in the provinces.

France’s national rail company SNCF says half of the country’s high speed trains are being cancelled. It says one out of three suburban trains are similarly affected. In Paris, half of all suburban train trips were hit.

Eurostar says its services linking London with Brussels, France and other cities are unaffected. Thalys, which runs trains between France, Belgium and Germany, told its customers to expect some disruptions.

Tuesday’s strike stems from a dispute with management over working hours, overtime, compensation and travel.