As has been said before, if you're about to do something like shoot a bunch of people, in a state that requires people to carry id and that has racist coppers who will stop brown people for no reason, it does not make sense not to carry id. You'd carry id, wear your seatbelt, obey the speed limit, all that stuff, to make sure you didn't fuck up on the way to the shooting.
So the only question would be why false id. If it was left by one of the shooters and it was false, given that their object was to cause division, it seems possible at least to think that they might purposely want people thinking they had come to France as Syrian refugees. Hell, the Daily Mail ran with this as their headline today. Even if it proves to be false, it has done damage.
Or... they were simply travelling on false id given that they reasoned their names were known to the authorities and a false Syrian passport was what was to hand.