You are technically right but the driving forces were France and Germany. Those two countries have a long history of wars and one of the goal of the European Coal and Steel Community, which started the whole thing, was to bring peace in the long term by ensuring close ties between the two countries. My grandfather who fought the Nazi in the French "resistance" once told me that whatever I thought politically about Europe, I should back it of all my weight because then I wouldn't have to see history repeat itself.