Health Minister Agnes Buzyn visited the resort yesterday to reassure residents and tourists there was a "very weak risk" of catching the virus.
The five new victims were taken to hospital in the Savoie region, but are not considered to be seriously ill.
Associated Press reports officials were now testing hundreds of children and their families in Contamines-Montjoie.
According to the BBC, authorities are closing two schools next week, both of which are attended by the nine-year-old child with the virus.
The boy lives in the ski resort of Contamines-Montjoie with his family.
In Spain, authorities were working to identify everyone who came into contact with a British man whose case was detected in Mallorca, a popular vacation island in the Mediterranean Sea.
According to Spain's National Microbiology Centre, the man contracted the virus at the end of January at a French ski resort.
However it has not been confirmed whether that resort was Contamines-Montjoie.
-with additional AP reporting