The US isn't doing anything in Libya . The French and Brits might. Going rouge would help them get out of the US shadow, clean up the image, restore some pride, make some frenamies, and they may even make a few bucks.
Both leaders could use a win, particularly a foreign policy win.
Anti armor weapons and heavy machine guns will change the air dominance situation without handing out stingers (advisors should bring them if they are on the ground without a no-fly zone).
Radios, intel, and advisors might change the dynamics from a disorganized bunch loosing the fight to a semi disorganized quasi-asymetric-gurilla-tribal alliance. hahaha It won’t cost much either.
Too bad the first Brits to hit the ground got thrown in jail. That may have altered their decision making prognosis. Certainly hasn't hurt the French narrative. I think they are both itching to stretch their legs. We’ll see if they have the nerve to take the risks involved with this type of operation soon enough.