Final answer:
The Bourbon family took over the throne of France after Catherine de Medici's sons failed to produce heirs to continue their lineage. Henry IV, the first Bourbon king, ascended to the throne after converting to Catholicism. The Bourbon dynasty was solidified by rulers like Louis XIV and reinstated with Louis XVIII after the Congress of Vienna.
Step-by-step explanation:
Although three of Catherine de Medici's sons became kings of France, they never produced the offspring necessary to prevent the throne of France from being taken over by the Bourbon family. The Bourbon dynasty came into power in France following the death of Henry III, the last Valois king. After the War of the Three Henrys and the associated turmoil, the Protestant Henry of Navarre, who was next in the line of succession, converted to Catholicism and became Henry IV, the first Bourbon king of France. His rule and the subsequent reigns of his successors, including the well-known Louis XIV, the "Sun King", solidified the Bourbon dynasty's hold on the French throne. Despite the efforts of Talleyrand at the Congress of Vienna to restore and advocate for the Bourbon monarchy with the return of Louis XVIII after the fall of Napoleon, the legacy of the Bourbons remained significant in European history.