Le Rapport  : House of Commons, Foreign Affairs Committee
Libya : Examination of intervention and collapse and the UK’s future policy options- Third Report of Session 2016–17.
(pages 10-11) :

20. A further insight into French motivations was provided in a freedom of information disclosure by the United States State Department in December 2015. On 2 April 2011, Sidney Blumenthal, adviser and unofficial intelligence analyst to the then United States Secretary of State Hillary Clinton, reported this conversation with French intelligence officers to the Secretary of State :

According to these individuals Sarkozy’s plans are driven by the following issues :
a. A desire to gain a greater share of Libya oil production,
b. Increase French influence in North Africa,
c. Improve his internal political situation in France,
d. Provide the French military with an opportunity to reassert its position in the world,
e. Address the concern of his advisors over Qaddafi’s long term plans to supplant France as the dominant power in Francophone Africa.46

The sum of four of the five factors identified by Sidney Blumenthal equated to the French national interest. The fifth factor was President Sarkozy’s political self-interes. http://www.solidariteetprogres.org/IMG/pdf/119.pdf