Finny is seeking reassurance. Gene's visit to Finny's home shook Finny's basic belief that all people are basically good. Finny was always a straightforward person and did not see duplicity in others. That Gene confessed to betraying him was a blow worse than the actual injury.
Over time, with distance, and with the predictability of the Fall school term, Finny had almost convinced himself that Gene had not been in his right mind during his visit. In order to reassure himself that things were all right, Finny placed the long-distance call to Gene. He needed to know that his best friend was still in place, and that he himself had not been forgotten or replaced. He also needed to save himself a place in Gene's approach to life. He reminds Gene not to start following the rules and imposes upon him the requirement to become a great athlete, since he could no longer fulfill that role himself.
Finny telephones Gene because he wants to make sure that Gene is all right, and that their friendship is still intact. The last time Finny had seen Gene was when Gene had visited him in the hospital. Gene, overcome by guilt, had told Finny that he had deliberately caused the accident that crippled him. Finny had refused to believe Gene, and the two had fought (Chapter 5).
When Finny and Gene finally connect again by phone, Finny is his old self, speaking with "friendliness (and) simple outgoing affection". He asks if Gene has a new roommate, and when Gene replies that he does not, Finny assumes it is because Gene has not allowed them to replace Finny. Even though this is not quite true, Finny is reassured that their friendship remains as it was before. He tells Gene that Gene was "crazy" when he visited at the hospital, and apologizes for having "just a trace of a doubt" about Gene's loyalty to him (Chapter 6).