They basically did. The French, however, under General Trochu and Favre, declared a military provisional government to continue the struggle. They agreed to a brief armistice with Bismark but when the latter demanded European concessions, notably a frontier buffer state between Germany and France, the war renewed in early September. A guerre à outrance was declared, basically a guerrilla war with the regular men of France rising up in arms. The Germans would surround and siege Paris while French guerrilla forces wreaked (ultimately fruitless) havoc on the rear lines of the German forces.
This completely changed the name of the game for Bismark and Germany as a whole. Within weeks over half a million Frenchmen would be mobilized again and they were barely holding onto Paris. However none of these armies could break through and break the siege. With no naval routes to provide food to the city, and numerous attempted revolutions already leading to at least 10,000 dead, the government capitulated. Afterwards Trochu's government disbanded and elections would ensue under the Third Republic.