You'd probably need more micro-states : the downfall of ancient Republics like Rome is often tied to their sheer size and the conflicts between growing bureaucracy and military power.
Maybe if the Holy Roman Empire reforms of the XVth century fails, you might end up with Germany looking like Italy, and without a strong imperial power to distribute titles and honors as they did in the peninsula, both Italian and German states could have kept/adopted republican regimes eventually. After all,it's what happen for Switzerland.
But unification and centralisation of bureaucratic states make monarchical (up to reasons, as
@CaliBoy1990 said) polities more likely to blossom. For entities like France or Burgundy maybe some extended regency where the Parliments/Estates/etc. end up to manage administration could lead to an "uncrowned kingdom", a republic in fact?