Europe isn't one country, and there is differences between places on which colour was picked.

The Netherlands was an early adopter and they picked red. So countries close to the NL (like Germany and Flanders in Belgium) and countries inspired by the Netherlands also defaulted to red.

Denmark went with blue, which is also in turn inspiring some countries to go with blue instead of red.

France seems to have gone with green, and by extention I've seen quite a few green bikepaths in the Francophone sphere. (Though Paris seems to have gone with purple for some of its paths?)

It doesn't really matter which colour is picked, as long as it is distinctive colour that clearly communicates that this is a space for cyclists.