If you consider Finny the tragic hero of the novel, here are the tragic elements regarding his characterization.
1. A once noble hero experiences a downfall: Finny was once the most popular, athletic student at Devon. He has everyone under his control--even the professors cannot resist his charm and sense of humor. However, after his literal fall, Finny also falls figuratively from his high position. He is now longer able to participate actively in sports and games, and his attitude has fall from overly optimistic to one of cynicism.
2. The tragic hero's downfall is caused by his own tragic flaw: While Finny truly is a decent young man who seems to embrace everyone, he is also oblivious to the reality of life. Before his injury, he glorifies the war and cannot wait to be a part of it. He also trust Gene completely and does not pick up on Gene's moodiness and envy.
3. The tragic hero experiences a tragic realization, usually before his death or the death of someone close to him. After Finny breaks his leg the second time, he finally admits to himself that Gene caused his first injury and considers why. He also tells Gene the truth about his writing all the different countries to see if they would allow him to serve in their armed forces. Right before his death, he has made peace with that issue and also with Gene.
4. The tragic hero ultimately loses much of what he holds dear. Near the novel's end, Finny loses his friendship with Gene (briefly), loses his health with another bad break, loses his dream, and ultimately loses his life.