As far as i understand it, in the Conference of Villafranca, Napoleon III didn't consult Piedmont-Sardinia. Wouldn't disregarding the Piedmontese in the peace treaty void the terms of the defensive alliance?
Napoleon III intervened militarily to defend Sardinia-Piedmont(later hoping to obtain an influence in Italy). After the war, Cavour gave the Savoy and Nice(the city where Garibaldi was born), the Government was absolutely aware, the People and Parliament were not. Somehow the Kingdom had to repay the help of the French.