French Ecology Minister Delphine Batho said there was no health risk after she visited the factory in the northern city of Rouen in Normandy.
Thousands of people, from as far away as Paris and London, have complained of nausea and headaches.
The gas is mercaptan, an additive to natural gas said to be harmless.
It leaked on Monday from a plant run by a French subsidiary of the US chemicals manufacturer Lubrizol near Rouen, 75 miles (120km) north-west of Paris.
Winds blew the cloud over northern France on Monday night and then into England on Tuesday.
Ms Batho cut short an official trip to Berlin to supervise emergency operations to stop the leak.
"I'm reassured," she told reporters after visiting the factory on Tuesday.
Ms Batho added that operations could last several days: "I prefer that we take our time rather than take risks."
Authorities will investigate what caused the leak and whether the company should be held responsible, the ecology minister said.
Tuesday evening's French Cup football match between Rouen and Marseille has been postponed because of the stink.
"We did not want to find ourselves with 10,000 fans 2km (1.5 miles) from the factory and with no means of confining them or evacuating them if necessary," local government official Florence Gouache told AFP news agency.
A Rouen resident told Reuters news agency the stench pervaded his home; "You can't ventilate. There is nothing to do, it's constantly in the room and it's unbearable."
Another resident told AFP news agency: "This is horrible. I thought I was in a gas cylinder." Another said the air smelled of "rotten eggs".
There is no word on the cause of the leak. The factory has been closed.
It is a "Seveso" site - a classification named after an industrial leak in Italy in 1976 and entailing a high degree of supervision,
A senior executive at the factory, Pierre-Jean Payrouse, said stopping the leak could take until the evening.
In Britain, the Health Protection Agency said: "The smell drifting over Southern England today poses no risk to public health.
"The odour, which is similar to rotten eggs, has been noticed by people mainly in Kent, East and West Sussex and some parts of Surrey."
Emergency officials in southern Kent advised residents "to keep doors and windows closed due to a gas cloud".
Staff at a chemicals factory in north-western France are working to stop a gas leak that has spread a foul smell to Paris and south-east England.