From the Super Mario Wiki
Franklin Badge is an item in the EarthBound/Mother series, and an item in Super Smash Bros. Brawl and Super Smash Bros. for Nintendo 3DS / Wii U. In the EarthBound series, it could deflect electric based attacks back at the enemy, but its effects are slightly altered in Super Smash Bros. Brawl. In Super Smash Bros. Brawl, once it is collected, it will automatically cling to the player that picked it up. If a projectile is shot or thrown at a player wearing the Franklin Badge, it will automatically be deflected right back at the attacker. However, the effects will wear off after a while.
The appearance of the Franklin Badge in Super Smash Bros. Brawl does not match with the appearance of the item in any of the original games. The badge has a background picture of the northern hemisphere on it, as well as a large picture that says EarthBound's Japanese name, Mother. In EarthBound it didn't have any appearance because like most RPG games EarthBound doesn't have sprites for each item, so instead the item is based off the appearance of the Franklin Badge promotional item that came with the Mother 1 + 2 game that was only released in Japan. In the sequel Mother 3 the Franklin Badge reappears, and unlike EarthBound, Mother 3 has sprites for each item, but its appearance is completely different from Super Smash Bros. Brawl, looking like a yellow badge with a grey bolt.
Super Smash Bros. Brawl