Finny's influence over Gene certainly plays a role in Gene not doing well on his test; however, it is mostly Gene's fault. Finny did not force Gene to go on the trip to the beach--if Gene had just stood up for himself, he could have said no, and stayed home to study. Gene as a bit of a weak character when it comes to saying no to Finny, and he needs to take responsibility for that, and not blame the amiable Finny.
Because of the beach trip, Gene does not have time to study, and does indeed fail a test. Gene is super upset about this, and takes all of his bitterness out on Finny, concluding that Finny is distracting Gene on purpose in order to make him fail. Why would Finny do this? Because Finny is jealous of Gene's good grades (not a strong point for Finny), and wants to "level the playing field." Finny is just as envious and bitter about Gene as Gene is about Finny. At least, these are the conclusions that Gene draws. Gene concludes bitterly that "Finny had deliberately set out to wreck my studies," and from then on, makes a more concerted effort to do well.
Whether or not Finny did that on purpose or not is up in questions still--Gene thinks it was, but as the reader it is hard to believe it. Finny just seems like a nice kid who likes having Gene around; after all, in chapter three, he confessed that Gene is his best friend. Eventually, Gene changes his opinion, but it is too late, after damage has been done. I hope that helped; good luck!