Franklin was actually a well-made character as far as his image, expressions, and mannerisms were concerned. He was a very convincing modern-day, LA-style, black gangbanger, that was all good. What messed up his character was Rockstar bizarre and stupid decision to give him mediocre involvement for most of the main story when he was supposed to be one of the protagonists. Also, the fact that Rockstar included very little gang and hood stuff in the game did not help his cause - this effectively meant Franklin could not even have his own significance through his own side story or side missions. He was doomed to fade in the background from the start, and it was such a shame, because he had so much potential to create some really exciting and interesting stuff in the game.
This is what I would do to make him better :
* Include much more detailed gang and hood action in the story that is almost exclusively centered around him. In fact, give him his own story within the main story that focuses on gangs and the hood and is longer in length.
* For him to be heavily involved in drug trade within story, and have many dealings and conflict with Hispanic gangs regarding this.
* Not wanting to leave the hood so soon to hook up with Michael, Trevor and Lester.
* Much more and deeper involvement with Simeon Yetarin. Maybe help him fight rival Armenian gangs, and run big luxury car theft rings.
* Show much more interaction and deeper relationships between him and the other characters from his world like Lamar, Stretch, Tanisha and his auntie. Especially Tanisha too, show some more of the history between them, and maybe some kind of a part where he tries to win her back with his high earnings from crime.
* Give him a nice array of infinite, decent side criminal missions and activities that reflect his world. Gang wars, gang recruitment, drug-dealing and selling, organized vehicle theft, gambling, like ghetto dice games, nightclubbing, dancing, gym, hood basketball games, better clothing options like expensive jewelry, better range of haircuts and styles etc.
* Reduce his association with Michael and Trevor, mostly seeing them when they gotta get together to do heists. Space out the heists far enough between each other to achieve this.
* Make it harder for him to earn big money until more toward the end. Before then, he'll be more fired up and hungry to make money from all kinds of crime, not just heists. He will still be heavily involved in gangs, drug-dealing, low-scale robberies like robbing stores to try and make fast money.
* Make him create and shape his own wealth. Buying and customizing his own safehouse properties, not have it being given to him by Lester. Buying businesses more relevant to him and his world, like his own LS Customs-style car garage business, a hip hop club/bar, a music studio, a soul food restaurant, stuff that adds more to his flavor.