"Yes, I am busy on weekdays."
I assume he didn't mean "in front of", but "after", as this makes more sense.
The topic in this case is not "I/私", it's only the subject. You can roughly translate it like this:
Speaking of weekdays, I am busy (then).
The red part is the topic, as this is what you're supposed to talk about if you answer a question like "Are you busy on the weekdays?". Depending on the context, this could maybe be omitted, but as we can't see the question, it is kind of essential. And we're here to learn sentence structure as well, so it's better this way.
The blue part is the subject. If I am the one who's busy, then 私 is the subject. This is most likely to be omitted, as it is obvious for Japanese people that you're talking about yourself if you don't include a subject. This has been said in this forum many times before, I know... but I just don't want to omit important stuff. ;)