The Italians typically didn't like any single power taking a dominant position in Italy, especially (but not only) when that single power was foreign. The result would be the Italians uniting together and starting a number of wars against France in an attempt to remove them from the peninsula. Owning Naples and Milan is a massive advantage - France's traditional rivals (Spain, the HRE, England) would be none too happy about them having that much power, either.
Would the Italians really be that successful though? Look at Spain. The Spanish pretty much ran Italy for almost 2 centuries, so the French could pull off the same.
It depends on the POD. It's going to be hard for France to hold onto Naples against constant pressure from the Habsburgs and Italian states. France also has their own internal religious problems to deal with, can they really hold onto Naples against Spain at the height of their powers? I'd think French domination of Italy likely to be a temporary situation.