Napoleon I and Napoleon III were, despite the similarities, fundamentally different rulers. Both reached power through a coup d'etat against republican governments that they were sworn to defend; Napoleon I against the French Directory of the First French Republic in 1799 in his capacity as consul of that Republic, establishing the First French Empire. Napoleon III on the other hand seized power from the Second French Republic in 1851 in his capacity as President, establishing the Second French Empire.
There are many reasons why Europe acted differently to the two Napoleons though. Napoleon I inherited a war with the rest of Europe in which the French State had already committed itself to overturning the established order. All that Napoleon did was turn the Republic into an Empire, and use his military skill to take this now 'revolutionary' ideal to its logical extension, that is, domination of much of Europe. The powers of Europe, not wanting to be dominated, naturally took offence.
Napoleon III on the other hand inherited a state which no longer had aspirations of dominance over the rest of Europe, indeed it couldn't if it tried to. He consequently spent most of his time in charge developing France economically. The major European wars his France participated in were rarely if ever prosecuted for the sake of territory for France, and were all carried out with the participation of independent allies. As such he was never seen as a threat to the European order.
Sources can be provided on request.