Sadly, the leather industry in Florence isn't what it once was (you can read more about Florentine leather here). Commercialization and globalization means that most of the bags are not made from Italian quality leather anymore and many are massed produced (cheaply) abroad. That doesn't mean that the traditional methods of tanning, dying, and crafting leather bags and accessories are dead in Florence, it just means you have to look a little harder to find it. If you want something cheap and fun, stick to the leather stalls and bargain, bargain, bargain. If you want an one-of-a-kind, handcrafted leather masterpiece, however, you will want to visit two places in Florence -- The Leather School at Santa Croce and Digerolamo.
At The Leather School of Santa Croce you can actually watch artisans construct leather bags onsite. While the school uses traditional, non-chemical processes, their bag designs (in my opinion) are much more traditional and a bit dated (but it is still fun to watch). Like The Leather School, Digerolamo uses the high quality leathers and traditional processes, but Digerolamo's bags are gorgeous, innovative, and contemporary designs. Furthermore, Digerolamo only uses materials that are socially and environmentally sustainable. Simply put, these bags are gorgeous! The first time I visited the showroom in Florence I wanted them all! I took the Sophia and the Penelope with me to France and I can attest that these bags are as functional as they are beautiful. I especially loved that the Sophia can be used as a clutch, shoulder bag, and crossbody.
I highly recommend that if you want to buy a leather handbag in Florence you visit both The Leather School (which is much more of a tourist experience) and Digerolamo. If you aren't planning a trip to Florence, don't worry. Digerolamo ships internationally!