Hi, and thanks for your question!
I imagine you mean feelings of romantic kind? I definitely think he didn’t. Zoe was a means to his end, he needed someone leaking information to the press and someone he could relatively easy control. He thought that Zoe was that person and the minute she started asking uncomfortable questions and being more trouble than help, he killed her.
Frank also did say that everything in life is about sex, except that sex is about power and Frank loves having power over people, so I imagine he didn’t mind having sex with Zoe, but that was just another way to have power over Zoe and not an expression of his romantic feelings towards her.