Those pop-ups were some "Avast has blocked..." alerts for sure.
And yes, if you click on the "Learn more..." link in there, it will take you to a page that... erhhh... is not exactly to my taste.
But Avast will not pop-up any ads just like that. Avast distanced itself from such intrusive advertising and I do appreciate this attitude very much.
But to answer your question: as far as I know there is no such thing as subscribing with a monthly fee, sorry.
But, tbh, I really don't think you do need the paid version. Avast + Comodo FW is just a fine combination to keep you safe - you can run a Malwarebytes Antimalware Free scan once a week additionally and you are okay.
Cheers
Zyndstoff