The ministry's director of public health, Caroline McElnay spoke to Breakfast about the deadly virus.
The two confirmed cases were announced by the health minister, Agnes Buzyn. A third person was later confirmed.
The minister said she planned to hold daily press conferences on the issue.
"We see how hard it is in today's world to close the frontiers".
Fewer than two dozen cases in all have been confirmed outside mainland China, in Hong Kong, Macao, the US, South Korea, Japan, Singapore, Thailand, Taiwan and Vietnam. "We will probably have other cases".
Buzyn said speed in diagnosing new cases will be essential in slowing the spread of the virus.
The minister said she believes that one reason why France is the first European country to have confirmed cases is that it has developed a test allowing medics to rapidly diagnose those affected. "He's fine", she said. "We identified the first cases very quickly".
The WHO held a meeting on the virus in Geneva on Thursday but did not declare the outbreak an global emergency.
As of Friday, more than 800 people have been infected across China, with 177 in serious condition. That person is hospitalized in Bordeaux.
Transportation was shut down in Wuhan, the city of 11 million at the epicentre of the outbreak, and in at least 12 other cities in central China's Hubei province, encompassing a population bigger than that of New York, London, Paris and Moscow combined.
As reported by Le Monde, the announcement included particulars on the patient in Bordeaux, a 48-year-old man of Chinese origin who is in isolation at Bordeaux University Hospital.