I would respectfully disagree that Carly’s affair with Franco didn’t make sense. At the time Carly was reeling from the death of her best friend and confidante, Jason. It was also believed at the time that Franco & Jason were brothers. Carly convinced herself that being with Franco (as Jason’s brother) would bring her closer to the friend she missed so terribly. This is typical Carly. It was for this same reason that Carly was drawn to Drew Cain, not as a lover but as a friend. Even though she had inner doubts she quickly cozied up to Drew. Heck, if you go back even further one could see her first sexual encounter with Sonny was due to her relationship with Jason. Sonny was Jason’s best friend and he was hurting and in need of help and she readily obliged.
You could say much the same for Liz. She has always been prone to jump from one man to another (Zander, Ric, A.J., Jake Doe, etc.) so anyone in pants would be fair game. At the time that she & Franco started seeing each other she was in a very bad place as she had lost the person she thought was Jason (her obsession) to Sam and everyone was upset at her for keeping the truth hidden for months. She knew what it felt like to be the town pariah, as did Franco. He paid attention to her, he comforted her, and they developed a certain amount of kinship which later became love.
She had messed up so many times and everyone forgave her so she could forgive Franco for what he had done in the past. She attributed his bad acts to a brain tumor so the kidnapping of her son was a nonfactor.
Inherently good people can do some really bad and stupid things and be forgiven for them. You say you lost respect for Liz because of her association with Franco but I never had respect for her before because of her deceitful ways. This didn’t change my view of Carly because I saw it as just another of Carly’s impulsive actions that she is more prone to when she is not with Sonny.