Can you post a link/pic of the coupon? And what agency is it with?
With Avis, I've used a "free day on a 5+ rental" before and it worked like this:
1. Book for 7 days and the rate is the same as ~4.5-5 days of a standard daily rate.
2. They subtract 1/7th of the weekly rate for the free day coupon.
3. You pay 6/7 of the weekly rate, plus all taxes and fees.
So, for simplicity, if the normal daily rate is $140 and the weekly rate is $700 (5 x $140), the free day coupon would take off $100. Technically it's a free day on a week-long rental. But if you book for 6 days, the coupon takes off 1/6 of $700, or $116.67.