WI - Italy doesn't annex the Papal States?

What if instead of annexing the Papal states, Italy decides its relations with France are more important. Does it eventually become an Italian protectorate, become peacefully annexed, or does the Papal State remain independent?
 
This means (presumably) that France does not lose the Franco-Prussian War (or maybe does not even fight it), so there are a lot of butterflies there.
 
What if instead of annexing the Papal states, Italy decides its relations with France are more important. Does it eventually become an Italian protectorate, become peacefully annexed, or does the Papal State remain independent?
Define not annexing the Papal State. Allowing the Pope to continue controlling Latium? The land taken by the Expedition of the Thousand being returned to the Pope?
 
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