Authorities in the Maine-et-Loire region said the accident occurred late on Saturday when a balcony on the third floor of the recently-constructed building collapsed in the city of Angers.
They said four people were killed.
A spokesman for the city's University Hospital said 10 people injured in the accident were admitted, one of whom was in serious condition. Another four were treated at a clinic.
The Ouest France newspaper said those on the balcony were young people attending a housewarming party.
The duty manager at the hospital, Michel Pichon, told France Info radio that all the injured "were about 20 years old,