Arguably, none of the character's natural weapons fit the description of "weapon they are holding", so no extra attacks at all.
I do have to wonder why the character isn't carrying any weapons at all, in that case. Surely a double weapon would be suitable, as you could switch out which hand is currently holding it as a free action?
And by that logic, unarmed striker builds don't benefit from Haste, yes?
For what its worth, the PF version changes it to be applicable to any natural attacks or manufactured weapons.