Why do Italians say "Firenze" and most others "Florence" ?

This is a question that preoccupies me already for a while...
To give an idea of the confusion, here is the start of a site on Firenze's history; it's in Italian ... and a translation in English: Primi insediamenti accertati nella pianura fiorentina. Sono tracce di un popolo (forse i liguri) che aveva importanti rapporti commerciali con la Grecia e la Sardegna. In plain English: Traces have been found that, round 2000 B.C., the plain of Florentina was inhabited by a population being in close commercial relationship with both Greece and Sardinia.

One of my friends thinks that Fiorentina has become Firenze just because this fits the phonetics of Italian: (flor,flower) = fiore. So, words like Fior(entia), later, by phonetic reduction for the ending sounds [-tsia] > [-sja] >[-za]> Fiorenza > gradually became Fiorenze... but the other step?
How is to be explained the cut off of the –o and the change from [jo] to [i] in F[jo]renz(a/e) ??