It’s a weird thing, which I’ve considered from time to time. Many of the songs I love in English have almost nonsensical lyrics, and if you asked me what the some was about I’d probably have no idea.
Yet I mostly don’t get much enjoyment out of non-English music.
I think it partly depends on whether I feel like it matches the genre.
Pretty much any French rock/pop/rap that I’ve listened to has sounded horrible to me. Same goes for most Japanese Rock/PoP and particularly Rap/Hip-Hop. It just sounds really unnatural.
Yet Enka (japanese folk/blues) sounds natural to me. I wouldn’t listen to it all the time, but it doesn’t sound weird.
There are a couple of cool Japanese Punk and more alternative bands, and I can chill out to Southern All Stars. But almost all the mainstream stuff sounds just odd in Japanese - it’s like the rhythm and cadence are off.
(Half the interesting Japanese bands I’ve discovered have been from Graham on the Sunday Papers, and he lives in Jersey(?))
I’m quite happy to listen to cuban, spanish, south american tunes though. And something like Baba Yetu works fine for me.
I wonder if it’s because the culture is more unknown to me, and therefore the language seems to fit it. (I have no idea if it’s actually natural/correct).
Plus I rather liked Sigur Ros, and I think at least one of their albums was in an entirely made up language.
So, yeah, non-western music in non-English seems to work better for me than western music in non-English.
The problem is that all the old men and teenagers listen to it too, so I always feel uncomfortable taking my kids to any of the live events.
Never sure if they are more interested in videoing the kiddy characters or the kiddies watching them. 
PS/ RPS Japan represent!