The Libyan embassy in Paris was asked to step in after scuffles in two separate luxury hotels in the French capital, during which Hannibal Kadhafi allegedly produced a nine-millimetre handgun.
After the first incident a woman was treated for bruises in hospital and later filed suit claiming to have been beaten by Kadhafi. Kadhafi, who is in his late 20s, left Paris for Copenhagen on Wednesday after being questioned by police.
Police were trying to determine whether Kadhafi has a permit to carry a handgun, but sources said this "doesn't seem to be the case".
Kadhafi does not enjoy diplomatic immunity in France, according to the foreign ministry.
"Only those people accredited by France to represent their country or those on official visits to France benefit from diplomatic immunity," Pozzo di Borgo said.
"Mr Kadhafi does not fall into either of these two categories and therefore does not have diplomatic immunity," she explained.