Answer
No, Bernard Kouchner did not serve under President François Hollande. Kouchner's political career primarily spanned the presidencies of Jacques Chirac and Nicolas Sarkozy. He notably served as Minister of Health under Chirac from 2002 to 2005 and Foreign Minister under Sarkozy from 2007 to 2010. Hollande's presidency, on the other hand, took place from 2012 to 2017.