Avast Free is just that Free, and I have been using it for over 14 years for free. Yes you may get offers for other avast products or upgrade to paid versions of avast, but aren't obligated to do that.
The free registration should automatically update after a period of time (10 days after expiry), but you should still be protected. If you have the current version of avast free this should work just fine, if using a very old version of avast it may hiccup.
I got a notification when my registration had 12 days to go and I confirmed my level of protection (for avast free) and my re-registration was completed.