While any form of learning engagement will benefit your language proficiency, I think song lyrics should be considered carefully. Just like poetry, they play on words and meaning, and oftentimes express something in a way that no other native speaker would have done just for the sake of rhythm or metafores. On the other hand, if you are at almost native level, getting and research these kind of ambigouity probably helps crossing that tiny narrow gap to native even further.

I second this, personally I'm currently using French version of Khan Academy to upgrade my French (you just do something like fr.khanacademy.org). The French also have a lot of theoretic math resources available and it's what I vibe with at the moment. Whatever gets you to read, listen, learn.