@Mobius
The rivalry between the French and English is much the same way, we don't hate each other at all, but we have about 7-800 years of history, during most of which we were trying to invade each other, the Spanish and Dutch were also involved but you can rest assured that whilst both the English and the French will frequently poke fun at each other for various battles throughout history, it is done more out of 'poking fun' than racism on either side, it's kind of like a Scottish football supporter deliberately supporting the other side whenever England are playing, it just winds up those who are overly nationalistic.
Edit: And that's ignoring the fact that I don't think it's possible for the English or French or, indeed, most of Europe to be racist to each other, because we are all the same race, we've been inter-mixed for so long that most notable figures have their roots in several countries. It's kind of like saying that a Californian who says he hates Floridians is a racist, he isn't, he might be a bigot, but he isn't racist.