The youngster took off on his bike following a quarrel with his mother at their home in the neighbourhood of Nivelles (Walloon Brabant).
Two days later French police detained him in connection with a shoplifting incident. A French judge then placed him in an institution. The French authorities maintain that they alerted the Missing Persons Unit of the Belgian police, but the unit denies that they received any word from France.
The head of the Nivelles public prosecutor's office will now examine what went wrong. The French authorities have apologised for what they call "a misunderstanding."