maybe the calendar in question only has a week at a time displayed? but yeah, it sounds weird to me too.
The context of the sentence suggests that there's an event marked on a particular Friday on a calendar. In that case, it's fine.
No. The only time you might say "the Friday" in English is: It's the Friday after next.
This would only make sense in English if only one Friday was in your calendar and you were saying this to distinguish it from other Fridays that were not.