Louis Sarkozy, the son of the president and his second wife, Cecilia, was reportedly playing with a friend at the end of last week in the courtyard of the palace.
Their game became a bit boisterous and they started throwing objects at the officer.
She was hit on the cheek and, on discovering the identity of the culprit, complained to her supervisor.
After news of the incident reached the president he went to apologise to the policewoman.
It is not known what punishment was handed out to his son.
Louis Sarkozy lives in the US with his mother, who has now remarried.
One of Sarkozy’s other sons was recently in the news after he fell ill in Ukraine and needed to be flown home on a presidential jet.
In January, Pierre Sarkozy was working as a DJ at a private party in the resort city of Odessa when he was struck down by food poisoning.
Weekly newspaper Le Canard Enchaîné reported that the president’s oldest son was flown home on a Falcon jet from the presidential squadron at a cost of around €40,000 ($52,376).
The Elysée Palace said at the time the president covered part of the costs of the flight from his own pocket.