Napoleon III wasn't that agressive. Since Solferino, he was much reluctant to involve into another war in Europe, instead promoting diplomatic solutions. If war was declared in 1870, that was under the pressure of the warlike public opinion and of the war party within the court (Empress Eugénie and Foreign Minister Gramont), and don't forget that Napoleon III was then a sick man.
Had the Spanish crisis had happened before the elections of 1869, that war would surely not have happened.
One would point at foreign interventions, namely Mexico, but that were more colonial ventures than anything else, and were not the consequence of some warmongering policy like a Napoleon I would have done, but looked more like a prelude to the great age of colonialism.
As for a Italian cause, it's few likely. French continued presence was more a consequence of internal pressure from Catholics than a conviction of Napoleon III who said, answering to one of his ministers who had declared that France would never abandon Rome, ''In politics, one should never say never''.
What's more, since Cavour, the French alliance was a pillar of Italian foreign policy to keep the Austrians in check and in 1866, they didn't enter the war on Prussia's side without Napoleon III's tacit approval (ie French neutrality), the same kind of which allowed them to annex northern Papal states and the Neapolitan Kingdom in 1860.
If you want to have Prussia attacked, maybe you could play with a delayed Polish uprising, causing Russia going to war with Prussia over some clandestine Prussian support to Polish rebels; IOTL, Prussian liberals were seemingly in favour of Polish rebels and the Alvensleben Convention caused them to reject the budget, but Bismarck remained in power due to King William support, but ITTL, Bismarck could elect to support the Polish cause if that allowed to get South German support in some war of defense against Russia.