@floreana post-edit comment: see, that's your problem, you should be using the US International layout with dead keys ;-)
(I joke, you should use whatever you feel most comfortable with, but US Intl has all accent and diacritics available via composition and dead keys. One layout to rule them all.)
If you have a Compose key enabled, compose e = should give you the € symbol. Otherwise, you'll need to enable the eurosign:e option for the keyboard layout (not sure how it's done via GUI)