...and seeing if it's among them? I searched "recent French song releases" and got a Spotify playlist, for example (which I can't play due to lack of Spotify account, it turns out). Apart from that, if you can catch a sentence's worth of words next time you hear it, that's often enough to find the full song, as I suspect you already know. I've definitely found a couple songs by searching a few words to a sentence before - one I remember was playing in a store and I think I found it using a few words from the chorus.

Good luck!

~Z