The tragic case in Toulouse, southwestern France, is the latest in a series of high-profile crimes which have placed the issue of repeat offenders at the top of President François Hollande's security agenda.
Public prosecutor Michel Valet said the suspect in the Toulouse shooting, identified as Thierry C., had apparently killed his victim by firing a rifle shot through the door of the flat's bathroom, in which the girl's mother had fled with her three children after being attacked.
The bullet struck the three-year-old in the forehead. Alerted by neighbours, police intercepted the suspect leaving the flat with a bag containing an automatic pistol and a rifle.
"From what we have been able to establish, it seems his rage was triggered by a row about the cleaning of the flat," the prosecutor said Thierry C., whose two previous convictions included one for violent robbery, claimed the gun had gone off accidentally.
Hollande admitted last week that France's judicial system had to improve its handling of convicts with the potential to offend again.
"How can it be that a criminal who has served time in prison but evidently still represents a danger to society cannot be subject to surveillance or some form of control?" Hollande asked last week in a speech honouring two slain policewomen.
The officers were shot dead in June by Abdallah Boumezar, a serial offender who had only just been given a six-month suspended sentence for a violent attack on his own mother.
The issue of repeat offenders was also highlighted by this month's arrest of Sebastian Dutheil on charges of raping two 11-year-old girls and sexually assaulting three other minors on campsites in the Ardeche region of central France.
Dutheil, 32, had been convicted in 2000 of a serious sexual assault on a 15-year-old girl. As a result he was on a national DNA data base of criminals but had not been subject to any monitoring.
Following his arrest this month, his first victim came forward to express her fury.
"The whole point of me going to the police back then was to ensure he couldn't do the same thing to someone else," Estelle told BFM TV. "Now he's done it again, I'm really, really angry."
What, if anything, the government can do to avoid a repeat of this kind of situation is however far from clear.
With France's prisons already overflowing, Justice Minister Christiane Taubira has made it clear she does not regard tougher sentencing as an option on either practical or philosophical grounds.
Taubira is due to present proposals on the new administration's penal policy to her cabinet colleagues next week, but all the signs are that any significant reforms will be put off until a cross-party consultative committee completes its work on the subject, which will not be until the end of the year
Asked what was being done to implement Hollande's pledge, a spokesman for Taubira replied: "An analysis is under way as to how the president's proposals can be elaborated whilst respecting constitutional imperatives."
The Socialists' right-wing predecessors introduced legislation in 2008 which made it possible for violent criminals who have served 15 years or more to be detained in custody at the end of their sentences if they are considered to still represent a threat to society.
The legislation was watered down when France's constitutional committee ruled it could not apply to individuals convicted prior to the act being adopted.