How anybody can suggest that Phoenix and Franziska could possibly become a couple is beyond me. They LOATHE eath other. On Franziska's side, she basically blames him for the death/downfall of her entire family. She has been raised, from birth, to believe that winning and perfection are of utmost importance and if she fails at either that she is worthless. He utterly crushed this. He indirectly sent her father to his execution. Then he defeated her entire family and "drove" her brother to "suicide." Of course she hates him. I'm not trying to badmouth Phoenix here, I'm just saying that this is how she views him.

As for Phoenix, he states multiple times that people like Franziska disgust him. He flat-out says that he despises everything she stands for. She is selfish and prosecutes only for her family legacy and win-record, and he hates this. He also makes it very clear that he has no intention of giving her the benefit of the doubt and does not think she will ever change. This is evident at the end of JFA, when she is shocked that he doesn't care that his win record is ruined. She asks him how he can possibly be happy for losing. He dismisses her and responds that she will never understand. Franziska cannot learn how to live for others instead of herself from Phoenix because it is very obvious that he does not CARE if she changes, does not think it is possible, and has no intention of associating with her and trying to teach her the right path. Thus, anybody who can not help Franziska grow and become more mature is in my opinion a very bad match for her. It also shows he doesn't really care about her, making him a worse match.

However, there are a couple instances that can be interpreted as them showing compassion for each other. Neither of these scenes, in my interpretation of them, had anything to do with them caring about each other. Of course, it's subject to interpretation, and we can't say what they really intended, I'm just stating why I, personally, don't think these two instances are enough to make up for their obvious hatred for each other.

1. Phoenix brings her flowers in the hospital--My interpretation of this depends on the fact that de Killer told Phoenix that it was for Phoenix's sake that he shot Franziska. Phoenix, therefore, probably felt responsible for what happened to her and wanted to make it up to her. I thought it was a sort of "I'm sorry" gesture, not a "I'm in love with you" gesture. And of course, any concern he showed that she was shot was only natural--You don't need to be in love with a person to care that they got shot. I'd like to think Phoenix is a nice enough guy to visit somebody in the hospital when they get shot, regardless of who the somebody is.

2. She keeps his picture at the end--To be honest, when I played through this scene it never even crossed my mind that her keeping the card had anything to do with Phoenix at all. In the scene before this, she had been about to give up. She had been going to stop being a prosecutor and based on some things she said I wouldn't have even been surprised if she'd considered killing herself. However, by the end she'd decided to continue on. When she says she's going to keep the card so that she can give it back to Phoenix when she meets him in court again, I think the important part is that she's saying she's going to return and continue prosecuting. I thought it showed character development that she was going to continue on despite the fact that she was not perfect. In my opinion, this character development is cheapened when you say that she only kept the card because she loved Phoenix.

Of course, like I said, this is merely my interpretation, but I don't think my interpretation is any less likely than two people who obviously hate each other deciding they're in love.
A few other things to consider:
-In the second case, after Phoenix wins the trial, he rubs it in Franziska's face. Because of this, she whips him so hard that he falls unconcious. I think it's pretty sick to say that she hurt a guy until he fainted if she was in love with him :/
-In JFA overall, Phoenix does not have any sympathy for Franziska or try to understand her. He obviously does not care that she was raised by Manfred to believe, from birth, that if she was not perfect then she was not worthy of living. Phoenix does not try to understand what goes on in Franziska's life, as he just does not care about her in general.