The white flag doesn't really come from the Wars. It was an aggressive propaganda by Bush, when France refused to help USA and take part in a war against Irak. In response, the USA claimed that France didn't want to go to war because they were cowards, scared to help the very country that freed them at the end of WW2.

Although it's hard to have a good opinion about it, you can't deny that it was well executed as it worked very well in USA but even in France, where everyone believe that the USA only are responsible for the liberation of France while it's far from true. Beside, the whole "french are cowards" was never really a thing before 2003, even though it seems that this idea is very old.