French defense analyst Murielle Delaporte writes that France took an almost Rumsfeldian approach to the war in Mali:
The French approach is very much about how to intervene and to trigger coalition operations in order to stabilize the situation with regional partners, rather than to simply stay in place for a long time.
It is "shock and awe" to deter the enemy and to trigger space for coalition success, not "shock and awe" for the sake of staying.
France has obviously learned the lessons of both Afghanistan and Iraq, which is that foreign "stabilization" forces (particularly from the country responsible for initiating hostilities) end up getting bogged down in costly insurgencies.
The current French approach won't necessarily lead to a Mali that is unified and stable, but given a choice between a chaotic Mali with hundreds of dead militants and no French occupation force and a Mali with an on-the-march Islamist movement steadily making gains, it's a pretty clear choice. The trick, of course, is in the getting out. France currently has its full contingent (roughly 4,000 troops) in the country -- and they're still battling Islamist rebels.