I think you should do both, hearing (having fun with the language) and also learning your grammar. When I study a language, I work on my grammar for maybe 3 days a week, I try to understand the explanations, I use flash cards, I write down important points. I also learn both grammar and vocabulary this way. Then, after a while I go through the exercises, review what I got wrong (I also repeat the exercises if I don't have at least two thirds right, or if it is an important or very hard topic). But one day of the week is dedicated to leisure - I tend to watch movies or TV shows in my target language. I watch what I like, not worrying about the vocabulary or grammar, not worrying if I understand and not worrying about what vocabulary I might or might not learn. This keeps me going, and I am happy if I can follow along easily. If I can't, I put more effort in the language the following week.

You need both. Eventually you should know how to use the correct grammar without conscious effort, and that's the sort of knowledge you acquire by hearing or listening (or by writing examples and exercises, etc.). However, it's much harder to learn proper grammar this way, so the shortcut is to study it and learn the rules. Children acquire grammar just by "hearing", but they get constantly corrected by their parents etc. for quite a number of years before they get it right. So unless you have someone who can constantly correct you (which is also annoying as an adult), you should study the rules (together with examples and practice, of course).