Answer;
Napoleon lll was captured and republicans declared an end to the second empire.
The statement that best describes how the second empire became the third republic is the fact that Napoleon lll was captured and republicans declared an end to the second empire.
Explanation;
The French Second Empire was the Imperial Bonapartist regime of Emperor Napoleon III, that lasted from 1852 to 1870, between the Second Republic and the Third Republic, in France.
In 1870 a new constitution establishing a quasi-parliamentary regime was widely approved, but France's defeat at the Battle of Sedan in the Franco-Prussian War was followed by an uprising in Paris, which resulted in the overthrow of the government, then the abdication of Napoleon III, and the end of the second Empire.