What is the “Task Force Lafayette”? It is “the pseudonym” used by around ten persons who would be ready to go to Iraq in order to fight against the Islamic State (ANSA).
It is about French women and men. Almost all of them were in the armed forces (someone would be due to resign, according to France Info), having served in the “French Legion, Special Forces, infantry, Navy (ANSA).
They assure to be unpaid “volunteers” and not “mercenaries”. On this occasion, they “do not represent France” (ibidem). Here’s also why such a choice would be incompatible with the uniform of their country.
The mentioned pseudonym (Task Force Lafayette) would recall the name of the “unit they served in Afghanistan between 2009 and 2012” (France Info).