Depends on your effort and willingness to practice. Fluency is very subjective mind you. I know this isn't really an answer, but given that your base language is English, it's going to take long.. I think something like 3x longer than it would to become fluent in French?

It would depend on your determination, the time you'll spend learning the language, and, of course, your effort. If you'll only get lessons or depend on those lessons online it would take longer for you to be fluent with the language. I think you should do more research too. Research about those questions in your mind. If you really want to be fluent with Korean, I think it would be better if you'll have your teacher so that he/she can help you with what you really need. Having books or dictionaries sure will help you too. :)

I've read something that says it takes 2 years and 6 months for an English speaker to learn Korean. It's a lot easier if you focus on conversational Korean, I've seen some people waste time and effort on learning fomal Korean. Hope this helps a bit. :)