Here "nouă" is unambiguously a stressed pronoun in the dative case. It is optional. It emphasizes the unstressed pronoun "ne".
If the phrase would be "Nouă ne place foarte mult.", then "nouă" would be either a stressed pronoun like in the original phrase or the numeral nine, depending on the context:
Exersăm navigatul. Nouă ne place foarte mult. = We exercise sailing. We like it a lot.
Alegeți un număr! Nouă ne place foarte mult. = Choose a number! We like nine a lot.
Please also see this thread https://www.duolingo.com/comment/26129267, and the links at the end of my long comment.