This seems like a question that doesn't come with any obvious search terms. The English wiki-page talks about Florence, and the Italian one about Firenze. Never the twain shall meet. And yet, there it is, in the very first line of the English wiki:
Florence (Italian: Firenze [fiˈrɛntse] ( listen), alternate obsolete form: Fiorenza; Latin: Florentia)
In other words: we start with a Roman colony called Florentia (the region was of course Etruscan before it was Roman, but the Etruscans preferred to build their cities on tops of hills, which is why they founded Fiesole instead). After centuries of vulgate Latin and Italian, this l becomes an i, giving us "Fiorenza" and, to this day, Fiorentina. From there, it is easy to see why the Italians might drop the awkward o to end up with Firenza/Firenze. (The latter is the plural, if my memory of Italian grammar is correct. I'm not sure why the town would have a name in plural, though.)
Meanwhile, the rest of the world stuck with the original Latin, where Florentia becomes Florence in France, and via there in the rest of the world as well. Easy as pie. In fact, even in the internet age this was surprisingly easy.