Why wouldn't France try to make a difference in a front where they take the lead?
I've written in those calls for action after the November Paris Massacre that Egypt could be a powerful ally in that fight against ISIL in Libya.
Egypt seems primed to be led:
Egypt continues its tight border controls with Libya. Mainly Egypt wants to keep weapons and Islamic terrorists from entering Egypt and stop illegal migrants (some of them new recruits for ISIL in Libya) from crossing into Libya. Smugglers still get a lot of people and goods into and out of Libya using the fact that the 1,100 kilometer long border largely runs through thinly populated desert. The desert route is more expensive and many illegals cannot afford it. Egypt continues making public calls for international help, from anyone, to help stop the violence and chaos in neighboring Libya. Egypt has been making this appeal for most of the year. These appeals have, so far, been answered with silence. Egypt has carried out some unofficial air strikes but wants an “international effort” (at least one other nation besides Egypt) to carry out an open and official air support campaign. One of the two governments in Libya (the UN recognized one in Tobruk) also called for some international help and got the same response as Egypt.
And Libyans seem primed to ask for help despite the protests that they don't want to do that "at the moment," according to Libya's U.N. ambassador:
The U.N. Security Council on Wednesday endorsed a U.N.-brokered agreement among Libya's warring factions to form a national unity government, a deal Western powers hope will bring stability and help to combat a growing Islamic State presence.
Libya's U.N. ambassador, Ibrahim Dabbashi, said Libyan authorities have no plans to request Western air strikes against Islamic State militants anytime soon, if at all. He dismissed media reports citing him as saying the resolution would lead to a swift Libyan appeal for Western military intervention.
France has limited but good quality military power available. Why waste it in the the Iraq-Syria theater where a major French escalation can only raise their small role from a rounding error to bit player level?
Leading an effort against ISIL in Libya would reduce a lot of problems France has in the area, from their former colonies to ISIL to illegal mass migration.
UPDATE: See? We can handle whatever France wants to do in Syria:
"Over the past month, we've killed 10 ISIL leadership figures with targeted air strikes, including several external attack planners, some of whom are linked to the Paris attacks," said U.S. Army Colonel Steve Warren, a spokesman for the U.S.-led military campaign against Islamic State, also known by the acronym ISIL. "Others had designs on further attacking the West."
One of those killed was Abdul Qader Hakim, who facilitated the militants' external operations and had links to the Paris attack network, Warren said. He was killed in the northern Iraqi city of Mosul on Dec. 26.
Come on France! Take down ISIL in Libya!