Another way he could react is with a sense of freedom. Maybe he realizes that the village has been holding him back in some ways. He could explore the world outside the village, make new friends and allies, and learn new techniques, all while still having the goal of clearing his name and getting back at those who wronged him.
At first, Naruto is likely to be confused and hurt. He has always considered the Leaf village his home and the villagers his family, so being banished would be a huge shock. He might feel betrayed.