After hearing the news, his former classmates became very attentive.
Police sources told local media that the boy had refused to do his homework and was hit with a broom handle.
The boy's elder brother, sister and stepsister were all present at the time of the incident.
Although his mother was not there, she too has been arrested and was aware of what was going on, reports say.
The boy's death in the early hours of Sunday prompted a vigil in the centre of Mulhouse among residents who rallied round his parents.
But the family's initial accounts of what had happened and the ensuing post-mortem examination prompted police to continue their investigation. Bruises were discovered on the boy's body, particularly on his feet, according to Alsace website DNA.
Although he had suffered a cardiac arrest, pathologists said the cause of death had been the blows he had suffered, DNA reported.
A police source was quoted as saying he had been struck by blunt objects.
The boy's mother had been away from home on a business trip but had actively encouraged his punishment because he did not want to do his homework, French media said.