Perhaps the main antagonist could be a new character. This new character could be an ancient evil that has been awakened by the presence of the Saiyans on Earth. They see Bardock and Raditz as a threat to their plans of taking over the universe and thus try to eliminate them.
In the 'Bardock Saves Raditz' fanfic, perhaps Bardock discovers a way to time - travel. He goes back to the moment when Raditz is about to die. Bardock could use his own power to shield Raditz from Goku's Kamehameha. Then, they team up and start exploring other planets, trying to find a new place for the Saiyans to thrive, away from Frieza's tyranny.
Frieza could be a great antagonist. Since Raditz is now part of the Dragon Team, Frieza might see this as a threat and decide to target Earth. His powerful forces and his own desire for universal domination would put him in direct conflict with the Dragon Team and Raditz, who has a personal vendetta against Frieza for the oppression of the Saiyans.
It could be a story of redemption for Raditz. He starts off as a bit of a villain, but through interactions with Bardock (either as a memory or some kind of spirit guidance) and Goku's influence, he changes his ways. They could all be training together on Planet Vegeta before its destruction, with Bardock teaching them valuable Saiyan combat techniques and life lessons that shape them into the characters we know.
Bardock's power could be shown as more raw and instinctive. Since he was a pure - blooded Saiyan from a time when Saiyans were more about brute force and conquering. Raditz might have a power level that is in between Bardock and Goku. His power could be more focused on intimidation at first, but as the fanfic progresses, he could develop it further. Goku's power, on the other hand, would be more about growth and adaptability. He learns from his battles and constantly improves, so his power could be shown as evolving more rapidly than the others.
It could be a new, self - made villain. Maybe a rogue ninja who was once rejected by the Hidden Leaf Village. He blames Naruto for his misfortunes and decides to target his sister as revenge. This villain would have his own set of unique and dangerous jutsu, which Naruto would have to figure out how to counter in order to save his sister.
It could be a rival archer who has a vendetta against the main archer and decides to target his family to get back at him.
One idea could be to focus on Bardock's perspective before his fateful battle. Maybe explore his thoughts about his son Goku being sent to Earth and his own impending doom. He could have some premonitions about Goku's future role in saving the universe.
Maybe Kabuto. He's a sly character who often works for the more powerful villains. He could be sent to capture Naruto's younger self for some experiment or to gain information. Naruto would need to fight against Kabuto's medical ninjutsu and his sneaky tactics to save his younger self.
It could be a rogue ninja from the Hidden Leaf's past who has come back for revenge. Maybe someone who was wronged by the village long ago and has now amassed great power to destroy it. Another possibility is a new enemy from outside the village, like a powerful warlord from a far - off land who wants to conquer the Hidden Leaf for its resources.
I haven't read this particular fanfic directly, but generally, in a 'bardock saves broly' fanfic, it might involve Bardock using his combat skills and intuition. Bardock, being a Saiyan, has a certain level of power and tenacity. He could potentially save Broly from some sort of danger, like a powerful enemy or a life - threatening situation on their home planet. It could also explore the relationship between the two Saiyans, perhaps Bardock seeing potential in Broly or having a sense of kinship towards him.