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First, you have to set your AltGr key(s). Go to System → Preferences → Keyboard → Layout Options → Third level choosers. In this section, you select what key(s) will be used as "AltGr". (I prefer the Right Alt).

Your keyboard layout(s) may not include the Euro Sign, so you may need to add it to certain keys. You do that go to Layout Options → Adding the EuroSign to certain keys. Select the key(s) you want to add the EuroSign to. Choose one that suits your keyboard.

It should be working by now. Open a text editor and test wether the Euro Sign is generated by pressing the "AltGr"+"EuroSign" key combination you defined in the previous steps.