Final answer:
The Capetian dynasty rose to power in France in the 900s, succeeding the Carolingian dynasty and laying the groundwork for ongoing French centralization and royal authority.
Step-by-step explanation:
The family that rose to power in France in the 900s was the Capetian dynasty. After the fall of the Roman Empire, the Merovingian dynasty established control over the region, with Clovis I uniting the Frankish tribes. The Merovingians were eventually succeeded by the Carolingian dynasty, beginning with Pepin the Short, who secured papal endorsement for his rule. This dynasty included Charlemagne, who further expanded the Frankish empire. However, the Carolingian dynasty faced issues with succession laws that fractured their territories after each generation. Finally, the Capetian dynasty took over after the last Carolingian king, effectively starting their rule with Hugh Capet's ascension to the French throne in 987 AD, solidifying their power through centralization and expansion of royal control.