French President Francois Hollande declined to answer when asked whether he was "still" having an affair with actress Julie Gayet.
The Daily Telegraph's Senior Political Correspondent Christopher Hope asked the President: "Do you think your private life has made France an international joke? Are you still having an affair with Julie Gayet? And do you wish she was here?"
The build-up to today's Anglo-French summit was dominated by allegations about Mr Hollande's private life.
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Investigators believe Mr Kushner has significant information relevant to their inquiry, officials told NBC News.
The men were detained as part of an investigation by MI5 and the Metropolitan Police's Counter Terrorism Command.