Question

What events led napoleon 3 to declare war on Prussia

Answer 1

Your best way to research an answer to this question is to look up something called the Ems Telegram.  Here's a short version of the story.

The throne of Spain was vacant, and a prince of the Hohenzollern family, a relative of the king of Prussia, was proposed as a candidate for the throne.  The French were alarmed at the thought of having a Prussian royal family member being considered for ruling Spain, their southern neighbor.  The Prussians withdrew the idea of Prince Leopold's candidacy.  The French ambassador to Prussia approached King William I of Prussia at the resort spa of Bad Ems, asking for an assurance that no other members of the Prussian royal family would be put forth as a candidate for the Spanish throne.  The king politely refused to make such a promise, and the discussion between them ended, and a telegram about what had happened was sent to Otto von Bismarck, King William's chief government minister.

Bismarck edited the telegram to make it sound as if King William had insulted the French ambassador, and had that edited version of the telegram published.  In the tense relations between France and Prussia, the publishing of this less-than-accurate account of the encounter between the French ambassador and the Prussian king was enough to provoke France under Napoleon III into declaring war on Prussia.  That was a mistake for France, because Prussia soundly defeated them.