The new rules are due to be unveiled shortly, but in the meantime, the government told local authorities to capture threatening animals, and, if necessary, put them down. France imposed initial restrictions in 1999, ordering dangerous dogs to be muzzled and always kept on a leash.
But the latest attacks have forced the authorities to review the original danger lists, which did not include cross-breeds.
"There are dogs which at present are not considered dangerous that are going to be put on the dangerous dog list," Agriculture Minister Dominique Bussereau told reporters after a cabinet meeting.
A 17-month-old girl died earlier this month after being bitten on the head by an American Staffordshire Terrier which was owned by her uncle. At the end of May, an eight-year-old boy died after being bitten on the neck by a Bull Mastiff.
The Interior Ministry estimates there are some 80,000 dangerous dogs in France.
However, some animal experts have questioned the government's planned clampdown, saying even docile breeds of dogs can be trained to become violent.