Classical civlization, spread through the conquests of the Roman Empire, was not shattered by the migrations of the so-called "Barbarians" in the 5th century; it was shattered by the Arab Muslims, whose victories in the Middle East and Northern Africa destroyed Roman civilization in those areas and severed Europe from economic and cultural contacts with the East.
In Pirenne's revolutionary work, he describes the last gasp of classical civilization in Europe, and its subsequent replacement by a primitive medieval culture.