K. asked : Why isn't the adverb "heureusement" used instead of "heureux"?

Dear K.,

That's a very interesting question!

The fact is that heureusement in French is actually a false friend, meaning "luckily"!

So while in English you say "they lived happily", in French we colloquially say "They lived happy", like "they were happy for the rest of their lives". 

I hope that answers your question!
À bientôt !