Hugh Capet succeeds Carolingian King Louis V, becoming the first King of the Franks and founding the Capetian dynasty of France. Hugh is elected king by an assembly of Frankish nobles.
He does not, however, ever use the title King of France — that title doesn't come into use until his descendant, Philip II Augustus. Nevertheless, most scholars regard the reign of Hugh Capet as the beginning of modern France because is Count of Paris and bases himself in Paris.
After this point, Frankish kings will start exerting more and more influence over the rest of the region, always using Paris as the center of political and economic power.
In the meantime, Hugh Capet is just King of the Franks and rules over a portion of what was once the Carolingian Empire. While Hugh rules in the west, his cousins, first Otto II then later Otto III, rule the eastern Frankish kingdom.