A man has been taken into custody on suspicion of having fired the deadly shot.
The police were called to the apartment in the Empalot area of Toulouse at around 5.15pm on Monday and arrived to find the girl, named as Shaloma C, bleeding profusely from a head wound, according to a report in the La Dépêche du Midi newspaper.
Despite the efforts of the emergency services, the toddler's life could not be saved and she died in the apartment.
The suspect, who is reported to be a man in his thirties, has been identified as the Shaloma's mother's current boyfriend.
The mother and her two other children were taken to hospital and received treatment for shock.
The shooting is reported to have occurred during an argument between the woman and the man although it has not yet been established whether the girl's death is the result of an accident of whether it was intentional.
Two firearms have been collected from the apartment.
A neighbour told the newspaper how she considered the family to be "good neighbours", reporting that while noises were heard from the apartment from time to time, "you would never have thought it would end with the death of a child".