Technically speaking, you're still incorrect. Algerian War happened inside the ECSC borders, however outside the European continent. Then, there were much small

Technically speaking, you're still incorrect. Algerian War happened inside the ECSC borders, however outside the European continent. Then, there were much smaller Basques-Spain and IRA-England conflicts. The right wording might be "there were not yet a war between internationally recognized acting EU member states". That may still be an achievement, because you cannot say the same for a lot of other alliances, e. g. for NATO.