Yes! Our Vespas are 125cc in Tuscany, Amalfi and Puglia. To be able to drive them in Italy, you need a car driving license (B) or a motorbike driving license (A). The AM licence is not sufficient. In Provence, you will drive a 50cc Vespa, there you need either a car driving license (B), a motorbike driving license (A) or the AM licence.
You must have a European driving licence. If you don't have one, you are obliged to have an international driving licence, which you can apply for in your country.