The EEC and the EU haven't kept Europe from having another two or three major wars since the fall of Nazi Germany. (Whether they could have started more world wars after the end of their empires is less clear). Outside powers imposing alliances that prevented the usual suspects from going to war with each other kept this from happening. Today, NATO keeps this from happening.
Some of their implicit goals were harmonising French and German interests so they wouldn't want to go to war again.
The closest I know of is the Cyprus conflict in 1974, but Greece wasn't an EU member then.
What are the two of three major wars which they have had? (Quite puzzled, as I have studied this a little).
He isn't saying those wars happened. He is saying the preventive cause is other then the EEC and the EU.
Obviously having massive troop presence prevented war with the soviets, but it can't be overestimated what stuff like the European Coal and Steel Community, the EEC and other following integration steps did after WWII in terms of getting France and Germany to "need" each other, instead of wanting "revenge" and repayment.