Post-Roman Europe as a cultural reference frame

I've been thinking for a while how it could be very interesting to explore a fantasy world that does not take it cultural background from the Renaissance, High Middle Ages, or Antiquity, but instead imagines an environment similar to Europe in the 6th and 7th century. Between the collapse of a centralized government and Roman administration apparatus and the conquests of the Carolingian dynasty in France, Germany, and the Low Countries. A period that really isn't Antiquity anymore without the Roman Empire as the superpower in Europe, but also does not yet match the image that comes to mind when thinking of the Middle Ages.

What are some things about this period in Europe that you think could make interesting elements for the worldbuilding of a fantasy campaign?