A gunman killed a teacher, his two sons and another child at a Jewish school in Toulouse on Monday morning before making his getaway on a scooter.
The victims were thought to include a rabbi who taught at the Ozar Hatorah school, his three and six-year-old sons and the headteacher's daughter.
It was at least the third deadly shooting in France in a week.
Investigators examined whether Monday's killings were linked to two deadly shooting attacks in the Toulouse region last week that killed three French paratroopers and left another seriously injured. French media reported that those paratroopers were of north African origin.
Interior Ministry spokesman Pierre-Henry Brandet said that the suspect in Monday's attack had worn a motorcycle helmet and made his getaway on a dark-coloured scooter - just as the assailant or assailants did in the two shootings last week.
And a gunman on a motorbike shot and killed a paratrooper in Toulouse on March 10.
Last Thursday a gunman on a motorbike opened fire on three uniformed paratroopers at a bank machine in Montauban, about 30 miles from Toulouse, killing two and critically wounding the other.
The Paris prosecutor's office said it would investigate eventual terrorist links to Monday's killing and the killings of paratroopers last week.
Speaking on behalf of the Conference of European Rabbis, Moscow Chief Rabbi Pinchas Goldschmidt said: "The thoughts of Jewish communities across Europe will be with the families of the victims."