Balkany, a rightwing politician who is a close political ally and personal friend of the president, claimed in a book he published last month that he had a fling with Bardot when he was 18 years old in the late 1960s.
Bardot would have been in her mid-30s at the time. She insists she met Balkany for the first time in 2004.
Balkany repeated the claim in a television show last weekend.
Bardot abandoned her film career in 1973, aged just 39, to take up animal rights activism. She has been prosecuted for inciting racial hatred by attacking what she called the "Islamisation" of France.
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