Why did the Battle of Sedan cause the fall of the Second Empire?

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The Battle of Sedan, fought on September 1, 1870, served as the catalyst for the collapse of the Second Empire primarily because it resulted in the decisive military defeat and capture of Napoleon III himself.12

Following a series of strategic failures, the French army under Marshal Patrice de Mac-Mahon was encircled and trapped by superior German forces at the fortress of Sedan. The subsequent surrender of the Emperor and his troops on September 2 was viewed as a profound national humiliation. When news of this catastrophe reached Paris on September 4, the imperial government lost all remaining legitimacy. Public outrage triggered a popular, largely bloodless uprising that led to the deposition of the Bonaparte dynasty and the proclamation of the Third Republic. This transition marked the end of the Second Empire, as the new government assumed power to continue the war effort against Germany.132