I don't really understand why people ask "Will an F in XXX hurt my chances?" Do you think your transcript would look better if the F were an A? Then you have your answer.
The only question is "how much will it hurt", and the only way to tell that is to know how close to the line you are. After all, it only makes a difference if it moves you from one side of the line to the other. The only way to know that is if we had your application and all the other applications. Since that's not going to happen, I don't see how we can quantify this.
That said, there are two red flags that this raises, and I think both are potentially more dangerous than an F. One is that it's an honors class that you're failing. The admissions committee will surely wonder why you didn't just transfer into the regular section. Not taking steps to rectify an academic problem looks bad. The other is your reason for doing poorly - if you do poorly when you don't find the material sufficiently enjoyable, I can tell you right now that grad school is not the place for you. There will be many times when you have to learn something that's Dull But Important. Learn it well. If you can't or won't do this, you will not succeed. Admissions committees do not want to admit people who they think won't succeed.