The kitten was adopted on October 25 from the streets of Argenteuil, about 15 kilometres northwest of Paris.
But three days later, it died and its owners were contacted by a vet, local police Gilles Prieto said.
The kitten was confirmed to have rabies, which France says has been officially eradicated from its territory since 2001. The strain of virus found had apparently stemmed from Morocco.
"Five people who were in contact with the kitten have been identified" and given preventive treatment, the health and agriculture ministries said in a joint statement.
Authorities are now trying to determine how the kitten got to Argenteuil. No other cases of animals showing similar symptoms have been reported.
The last case of rabies originating from within French territory was in December 1998 when a sick fox was found. Since then, cases have been sporadic and strains of the virus originating from elsewhere.
Only 10 countries and regions in the world are listed as rabies-free. Some 55,000 people die of the disease worldwide every year.
Symptoms in humans include seizures, partial paralysis, fever and brain inflammation, or encephalitis.
There is no known treatment to cure rabies once the infection has taken hold.