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15-year-old Louis, whose mother is Sarkozy's ex-wife Cecilia Ciganer, bombarded the unnamed officer as she paced the street outside the Élysée Palace.
According to Sky News, she was also hit on the cheek by a pellet as Louis and his friends played in the courtyard.
Police sources say that Sarkozy later met with the policewoman and apologised on his son's behalf.
However, his office declined to release a statement of their own.
Sarkozy also has two adult sons from his marriage to Ciganer, which ended in 2007 shortly after he was elected president.
He welcomed a baby girl named Giulia with new wife Carla Bruni last October. It marked the first occasion that a French president has had a child while in office.
> Carla Bruni: 'I'll do everything to protect new baby'
