Well, in fairness to the ignorant yokels on the left side of the Atlantic, [ pointing to the East ] They started it. [ hyperventilating and childish mode off ]
Specifically, de Gaulle made a point of spitting in the eye of U.S. policy throughout the late 1950s and early 1960s. Some of it was a legitimate desire to keep France from becoming a puppet of U.S. policy (although I’ve never seen Britain accused of that except by a few Brits since the WTC attack), but a substantial amount of it was simply a desire on the part of de Gaulle to pump up his own image. It came to a head in 1960, when de Gaulle asked snidely (paraphrase), “Why do you Americans stay where you are not wanted?” and was promptly savaged by Bill Mauldin in a cartoon that can be found at the top of this article in the Chicago Reader. (There were a lot of reminiscences by French folk in Normandy in 1994 that showed a lot of good will toward the Yanks, who might have only been passing by on the way to Germany, but who never left.)
The “rudenenss” stereotype is also pretty much without merit. There certainly are rude French (and more rude Parisians) just as there are rude Yanks (and more rude New Yorkers), but the vast majority of people are simply people. I toured France by myself at the height of the anti-American feeling prompted by the Vietnam conflict and the few rude people I encountered were just rude people, with no “national character” involved.
The jingoistic tendency of the English to consider the French cowards was common enough in 1887 for Gilbert and Sullivan (well Gilbert anyway) to parody it. In Ruddigore, “Dick Dauntless” the sailor sings a boastful song about how his ship encountered a French ship. They approach, intending to attack, but then they notice that the French ship is heavily armed. At that point the English ship decides that “to fight a French fal-lal, it’s like hitting of a gal. It’s a lubberly thing for to do,” and turns tail and runs. At the end Dick assumes that in relief “they kissed each others’ cheeks, which is what them furriners do, and they blessed their lucky stars we were hardy British tars who had pity on a poor ‘parly-vous.’”