Problem end subscription membership

Hello, I come to you because I do not find the solution
I have two types of subscription on my site, and a free limited and the other paying
When I do the test of the paid subscription, and it comes to an end: one week, the member remains the same subscription and continues to have access to all site content, though its membership is completed how do you do it automatically descend to the free subscription
In Subscription Plan, I put the first paid subscription: finite, one week and the amount
and I slipped under the free subscription: indefinite, 0 euros
Is this the right solution?