"President (Nicolas) Sarkozy sent a personal letter in his and his wife Carla's name in which he expresses his condolences to Prime Minister Benjamin Netanyahu and his spouse Sarah after the death of the latter's father," the official said, requesting anonymity.
"In the letter, Mr Sarkozy reminds the prime minister of his friendship and underlines that their differences over the problems of the Middle East, which the press echoed recently, do not have an impact on this friendship," said the official.
The Israeli government declined to comment.
In Paris, the Elysee confirmed that a "private" letter had been sent, but refused to disclose its contents.
Sarkozy famously called Netanyahu a liar during a private conversation with US President Barack Obama during the G20 summit in the French city of Cannes in early November, according to journalists.
The conversation was overheard by a number of journalists after it was inadvertently transmitted over a system used for translation, media website Arret sur Images reported.
"I can't stand him anymore, he's a liar," Sarkozy was heard to say in French.