PARIS—New virus variants are spreading fast in multiple regions of France, causing local authorities to order tougher mask rules and a curfew crackdown around the English Channel coast, and prompting growing calls for a new lockdown in the east. Although France closed its borders with Britain in December, the virus variant first identified in Kent, England is now responsible for a large majority of recent virus cases around the French port city of Dunkirk, according to a statement Saturday from the regional health agency. The regional administration ordered tougher mask rules and urged people in Dunkirk and some other areas not to leave town to limit the spread. The city’s saturated hospitals are sending COVID-19 patients to other regions amid a spike in the number of people needing intensive care. France’s national public health agency warned Thursday that the spreading variants could worsen the country’s virus situation in the coming …