The six – all women according to deputy mayor Caroline Pozmentier – died from smoke inhalation after the fire raged through the third floor of the building after breaking out in one room.
"The staff are in shock," said Pozmentier.
Firefighters treated 15 people for smoke inhalation. Three were in a serious condition and rushed to hospital.
"The fire broke out this morning around 2:30 am (0130 GMT). It was pretty fierce and limited to one room but the room's occupant has not died," deputy prosecutor Christophe Barret told the press.
"Three people are seriously injured and 10 injured more lightly as they suffered from less serious smoke inhalation," he added.
"The fire apparently broke out in one room which was totally gutted."
A total of 180 people were in the nursing home when the fire broke out but not all of them were evacuated.