Processes in Microsoft 365 for setting up Office apps, redeeming product keys, and activating licenses.
Are you able to cancel the free trial of Microsoft 365 using the steps provided on this link.
Then, where did you purchase the Microsoft 365 Family subscription, if you purchased that from a 3rd party retailer, were you provided with a product key, and if so, if you log into this link and enter your product key, is it accepted to start the new subscription.