Well this is a show about World History so let's look at the facts:

They've hated each other from the very start having a war that lasted 100 hundred years (no joke) plus the Nine Years' War (/Seven Years' War/French and Indian War).

At one point in time, in England, it was an insult to describe something as French.

History tells us this is not going to happen.

Yeah, guys, it's a complete bromance. The way they squabble is adorable, however, and I'm not opposed to reading any fanfics ;)