The French Army of Chalons was encircled at Sedan on September 1, 1870, and by the next morning it had ceased to exist. Napoleon III surrendered in person along with about 104,000 men and 558 guns. The capture of a reigning emperor decided the Franco-Prussian War in a single day, even though the fighting went on for another five months.
The army had not gone to Sedan to fight. Marshal Patrice de MacMahon was marching to relieve the fortress of Metz, where Marshal Bazaine's Army of the Rhine had been shut in since August 19. Moltke read the move, left two armies to hold the siege and took two more north, caught the French at Beaumont on August 30, and forced them into the town of Sedan on the Meuse. German artillery occupied the heights on three sides.
What followed was a killing ground. French cavalry under General Margueritte charged the village of Floing three separate times against concentrated Prussian infantry and gunfire. Margueritte was killed leading the first charge. MacMahon was wounded early and passed command through two officers in a few hours, so no coherent order to break out was ever carried out. French losses on the day ran to roughly 3,000 killed, 14,000 wounded and 21,000 captured. German losses were around 9,000 in total.
The political effect was faster than the military one. When the news reached Paris, crowds took to the streets, and on September 4 the Second Empire was abolished and the Third Republic proclaimed. Bismarck now had no French government with a mandate to negotiate, and the new republic refused to cede territory, so the war continued through the siege of Paris.
On January 18, 1871, the German princes proclaimed Wilhelm I of Prussia as German Emperor in the Hall of Mirrors at Versailles. The peace treaty that followed took Alsace and much of Lorraine from France.