The problem with the idea of US cars aping the appearance of European cars in the 1950's and early 1960's is that virtually all americans considered the vast majority of mass-market European cars cheap, underpowered, underequipped, and too small. There were niche exceptions to that rule, of course (sleek Italian sports cars, snappy little British roadsters, and a few luxury sedans), but in general before the fuel crunch began Americans would have considered any attempt to emulate European cars totally pointless.
The best chance for something radically different might be in the streamline movement - car shapes that were rounded, very glassy, and close to teardrop shaped. Obviously streamline movement vehicles looked better on paper than they worked in reality, but in the 1950's Americans cared less about how cars looked (assuming they at least ran and seemed heavy and solid) than how they actually worked.