How to pronounce “euclidean space” in English

You have Pythagoras' theorem for Euclidean space, and you have Minkowski's equation for relativistic spacetime.

and other geometric forms behave in hyperbolic space, which is different to the way they behave in Euclidean space.

Well, it's an alternative to the two kinds of geometries you're already very familiar with-- Euclidean geometry or Euclidean space, and spherical space.