Kill Garibaldi.
The original Plombieres Agreement didn't call for a united Italy. S-P was to receive Lombardia and Venetia only. Then a 'Central Italy' in Tuscany and bits of the Papal States, a continuing Pope-run state and Two Sicilies. However Garibaldi's populist message led to large volunteer units of Redshirts spreading throughout the pennisula specifically for Italian unification, most notably in the South. He effectively gave the Two Sicilies to Turin because he saw King Vittorio as the natural leader of a united Italy.
No Garibaldi blunts this upsurge of Italian nationalism. However there's probably still something there. If someone, a staunch republican like Mazzini ends leading the former Two Sicilies there's little chance of peaceful unification and Sardinian troops had a mixed reputation (remember in 1859 and 1866 Austria handed territory over to France officially because Vienna felt the Italians had not really won the wars). The Central Italy proposed at Plombieres was artificial and meant by the French to focus S-P against the Austrian controlled North. Realistically, due in part to fairly peaceful popular demand as IOTL it falls to Turin. So you end up with Upper Italy (name suggested at Plombieres), the Papal States and the Two Sicilies (kingdom or republic).
If a republic in Naples you could see Turin, Paris and Rome all keen to crush it. But the implications of what happens after might stay their hand. If the Pope has held onto territory the stretches across the pennisula, Napoleon III might be keen to continuing supporting the Papal States as a buffer while either telling Mazzini to shut up or using force to restore a kingdom - but the kings where Bourbon so...
Ultimately Italy unified against Napoleon's wishes due to the sheer speed and level of popular revolt encouraged by Garibaldi. If the 1859 War ends with three states, Napoleon III might just consider it a close run thing and attempt to maintain the status quo. For the future security of Rome he would not support a Sardinian invasion of the Two Sicilies post-1859.