Better than the French would be a Muslim nation that has a viable military. Turkey is one such example. The Turks do have a good military and they could be expected to be a neutral player. Probably more-so than the French who use to be a colonial power in this region and to this day have vested interests. While the Turks are now silent, I am sure sufficient funds for this peacekeeping mission would energize them.
People often think a Muslim nation would be better. However, if you pay attention they don't want that, because it would be like being conquered by a neighbor. They were all under Turkish domination for 400 yeaars of hte Ottoman empire and would not welcome return of the Turks.
On what planet would they be a neutral player?
I see them as islamics who will side with their bretheren when the chips are down.
This is one of the biggest problems with a long term solution -- there are no really neutral parties.