The futuristic city with flying cars at the beginning of the movie definitely has all the cyberpunk visuals, and technically Zorg is the head of an evil corporation. But the real villain of the movie is incoming force of evil/darkness. And the plot is resolved through the power of love. Even the President of Earth is actively trying to help do the right thing and save the planet.
While there are some great cyberpunk visuals at the beginning of the movie, I don't know if the themes are there to call this cyberpunk. What do you think? Would you consider The Fifth Element to be cyberpunk?
Been a while since I've seen it, but one thing that I'm remembering differently than a lot of folks in this thread is that I don't remember it being outright dystopian. Sure, evil corp and all. But Earth government isn't really evil, the arts are still cherished, and while life seems hard it seems more like a dysfunctional society than a dystopia. Just my take though (and doesn't address OP's question).
My fun anecdote is that maybe 10 years back I got a free LaserDisc player. The local library happened to have The Fifth Element on LD, so naturally I rented it. You had to request media at the front desk, so I wrote down the call number and he returned with a very confused look
"you know this is LaserDisc, not DVD or Blu-ray? Like, it's...really big." Not the same quality as Blu-ray, but was definitely more fun :)