Well, I think it's helpful to look at this in the broader geopolitical context.

1: Conflicts often arise when the balance of power is multipolar. That's how I would describe Europe during the years prior to the second World War.

2: After World War II, a couple key developments happened. The United States, which had been the largest economy in the world for a long time, had the largest military capabilities, and had emerged from World War II relatively unscathed, shifted away from it's historical isolationist policy toward Europe. Second, the Soviet Union emerged as the primary threat to the liberal democratic & free market ideals in the West. Even before the second World War, the Soviets were seen as a major threat, but Hitler's aggressiveness made it necessary that he would need to be taken care of first.

3: It wasn't long after 1945 that Britain learned it couldn't really conduct it's own foreign policy expeditions without American backing (see Suez, 1956). France was more difficult difficult. De Gaulle left the NATO command and kicked American troops out of his country, but he still viewed the Soviets as the primary threat.

4: West Germany had thousands of allied troops in the country. The country was split in two. It wasn't seen as a threat to France, which was a big driver of the last 100 years of European conflict.

5: A sidepoint on pt. 4, there was a lot of internal opposition to German reunification. Margaret Thatcher was bitterly opposed to German reunification. Mitterand opposed reunification as well, but he viewed it as inevitable (source). With the fall of the Soviet Union, there was fear that Europe would return to it's old ways. That never happened of course and I'd probably attribute that more to American presence on the continent than to economic integration. In a world where the United States is a dominant power willing to exercise power globally, war between major powers is impossible. Especially when those powers share the same values.

6: Europe since the Fall of the Soviet Union has increasingly come to a consensus of a "Western" foreign policy, probably dictated more by Washington than the Europeans would like. The American-British-French-German alliance is the closest between Great Powers in World History.

TLDR: I'd probably attribute it more to an American superpower devoted to stopping the Soviet Union by aligning itself with the European powers (West Germany, Britain, France) than to economic integration. If the United States had decided after 1945 to do what it had been a principle of American foreign policy and avoid entanglement in European affairs, then perhaps the last 65 years would look very different.