In the concluding chapter of A Separate Peace, after having returned to Devon School in order to resolve his internal conflicts of years ago, Gene Forrester narrates,

...it seemed clear that wars were not made by generations and their special stupidities,...wars were made instead by something ignorant in the human heart.

It is this fear in the human heart that causes countries to feel they have sighted an enemy, an enemy against whom they must prepare a defense.  And, so, like France that constructed a Maginot Line against its enemy, Gene realizes that he has constructed his own line of defence against his perceived rival, Phineas.  Thus, Gene discovers that his personal fear which drives him to injure Finny is much the same as the fearful evil that produces war. 

I never killed anybody and I never developed an intense level of hatred for the enemy (in the war). Because my war ended before I ever put on a uniform: I was on active duty all my time at school; I killed my enemy there.

Symbolically, therefore, World War II reflects the inner conflicts of Gene, as well as his external ones.  For, his internal fear drives him to wage a private war with Finny, a war of physical and mental ability.  His return to Devon School is his return to the private battleground of his essential war with himself, his envies, and resentments.  In short, at Devon, Gene comes vis-a-vis with his private horror; he emerges with "a separate peace" that is not tied to the world war.  So, while the title of Knowles's novel, "A Separate Peace" is from Ernest Hemingway's A Farewell to Arms in which the protagonist Lt. Frederic Henry "declares his own private armistice during World War I" (enotes), Gene's armistice is not literally connected to World War II, although it is symbolically.