Refers to one's overall fortune or luck, often in the context of fortune-telling, horoscopes, or general life outlook.
I had my fortune told for today.
He has strong luck.
I had a fortune teller read my fortune for this year.
My fortune today was really bad.
I look forward to checking my horoscope's fortune every morning.
Apparently my fortune will improve starting next month.
運勢 refers to one's fortune as told through horoscopes or divination, whereas フォーチュン is a borrowed word rarely used in ordinary speech.
運勢 refers to one's fortune or luck at a given time (as in horoscopes), while 運命 refers to one's overall predetermined destiny.
Compound of 運 (luck, fate) and 勢 (force, energy), suggesting the momentum or trend of one's fortune.