It's wrong. It should be: "이번 주 금요일이 며칠이죠?"

Hmm...are you trying to say what date is that Friday or what day in terms of holiday or special event? Date: 이번 금요일에/은 무슨 날짜예요? Special event /holiday: 이번 금요일에/은 무슨 날이에요? You don't have to say this week's Friday, as it is wordy in general. So just say "This friday..."

무슨 요일 - which day of the week; 며칠 - what day (in terms of date). Your sentence literally says "Which day of the week is Friday this week?", which obviously sounds silly...because the question answers itself...Friday! Also, 의 is usually omitted colloquially. So that's why it's 이번 주 금요일이 /며칠/이지요?