"I have a holiday on Saturday, so I have some free time that day." If you use "this day", it seems to imply "today". Saturday is a free day for the regular working Joe, so it sounds strange to call Saturday a holiday. If you normally work Saturdays, then you can simply say "I have a free day on Saturday," or "I have a day off on Saturday."

I have a day off on Saturday, So i have some free time then.