Learn about all different countries pupils represent, e.g. each class can research one country
Organise a fund raising day for an aid project
Educate the whole school about what the EU means for you personally and/or on a global scale.
Correspond with your local MEP, ask them for information, ask to be placed on their mailing list so you can keep informed about what they are up to, can you invite them to your school to speak?
Look into the buying habits of the school (fair trade, ethical consumption) What products, did you find in your review, are bought most regularly? Can you switch to fair trade products? Can the school start buying environmentally friendly cleaning products or recycled paper and/or copybooks?
Map changes in Ireland pre and after EU, are changes due to admission to EU or would they have happened anyway?
Carbon off-setting, you could plant a (native) tree to offset some of the carbon the school emits, reducing climate change problems for developing countries.
Free trade, what impacts are associated with free trade economy? (for example look at big supermarkets versus small local shops, identity of small villages in Ireland)
Mentoring project for Green Schools in other (EU) countries, help them with their Green-Schools programme and in exchange learn about their culture