Bastiat definitely embodies the "Harmonic" school of libertarians, who consider utilitarian and natural law arguments as two complementary aspects of a same world.
Bastiat did not take part in the anarchist vs minarchist debate (he arguably died too early for that); he seems to have considered State as something inevitable as far as immediate practical things matters, something that ought to be taken into account as long as it existed. He also explicitly opposed violent revolution as a way to get rid of governments.