It's not exactly the city centre but I bet the students would enjoy the varied menu, the prices, the space and the little bit of history that goes along with it.
You could also check out I Tarocchi along the Arno River, which I know works with many student groups but I am not sure of their capacity http://www.pizzeriaitarocchi-firenze.it
Another restaurant that I have used for large groups in the city centre, and I believe they have a large sala inside: http://www.ilbargello.it
