Apulia - Original Latin form of Puglia.
Bologna - In English as I know it, the name of the city has never been anything other than the Italian form, Bologna. Maybe you’re thinking of the sausage loaf that in colloquial American English has become “boloney,” especially when used metaphorically. Like, I think using French names in English is a lot of boloney.
Genoa - Neither French (Gênes) nor exactly modern Italian. I think it derives from a medieval variant form of Genova that was taken into English. If I’m not mistaken, the original Ligurian form was Genua.
Latium - Original Latin form of Lazio.
Leghorn - I always wondered about its development into the odd form it took in English. According to the Italian site Eracle, the name of Livorno/Leghorn derives from an ancient mythological figure, Ligure the son of King Fetente of the Molossi. (Probably the ancient forms of their names were Liguris and Fetentis.) The sound of [g] between vowels can often become elided into a glide. This has happened as a regular sound shift of the Turkish letter ğ, which began as [g] in earlier forms of Turkish, but has now been elided to a glide, either [j] or [w]. The shift of w>v in Italian is another regular sound shift. Does that make it clear? I don’t know how the -n got added to the end of the name. Anyway, it looks like Livorno shares the origin of its name with the region of Liguria. Although Livorno is currently in Tuscany, Livorno is near the border of Liguria. That part of northern Tuscany at Livorno was the southernmost reach of the Ligures area in pre-Roman times. Someone help me out here.
Mont Blanc - French form of Monte Bianco.
Padua - Another medieval variant form taken in by English, while in modern Italian it developed into Padova. From Latin Patavium.
Syracuse - French form of Συρακουσαι?
Trent - French form of Trento?
Trieste - I believe this name stays the same, whether English, French, or Italian!
Tuscany - Here the anglicized form of Toscana follows a medieval French model.
Vesuvius - Original Latin form of Vesuvio.