Mr Sarkozy invited Craig Stapleton to see him in 2006 to say how proud he was to meet President George W Bush.
He later introduced his nine-year-old son, Louis, who had "a small dog at his feet and a large rabbit in his arms".
When Louis put the rabbit down to shake hands, the dog started chasing it. Mr Sarkozy then had to run after the pets.
The incident is described in one of the 251,287 classified cables the whistle-blowing website Wikileaks says it has obtained and shared with several newspapers.
The "rare glimpse of a relaxed Sarkozy" came when Mr Stapleton visited the then interior minister at his office at Place Beauvau in Paris.
"Sarkozy went to the line of floor-to-ceiling windows that open from the interior minister's office to the gardens of the interior ministry, and called over... Louis, who was playing on the lawn," the cable says.
"Louis appeared at the threshold with a small dog at his feet and a large rabbit in his arms," it adds.
"To shake hands with the ambassador, Louis put down the rabbit - and the dog started chasing the rabbit through Sarkozy's office, which led to the unforgettable sight of Sarkozy, bent over, chasing the dog through the ante-room to his office as the dog chased the rabbit, and Louis filled the room with gleeful laughter."
Nicolas Sarkozy Chased Rabbit
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