The original Super Mario Kart (released in Europe on January 21, 1993) does not have a formal plot or "story mode". Instead, it serves as a friendly (but competitive) racing tournament held between the iconic characters of the Mushroom Kingdom.
The "EU" in is a misnomer in the sense that there wasn't a single "European" version. Because the European Union comprises dozens of languages, Nintendo produced multiple cartridges under the same PAL umbrella.