Ness makes his way to Happy Valley where Paula is being held prisoner. Ness visits her cell and she gives Ness the Franklin Badge, which will help in the battle against her captor.
From Wikipedia:
EarthBound, also known as EarthBound: The War Against Giygas! and released as in Japan, is a role-playing video game co-developed by Ape and HAL Laboratory and published by Nintendo for the Super Nintendo Entertainment System video game console. Learn about Earthbound