[REAL, 1961] Citroën Ami
More info and pictures of the different bodystyles can be found on Wikipedia:
https://en.wikipedia.org/wiki/Citroën_Ami
It really looks like it'd have been easier to design, manufacture, and more functional, if they had left that bit in, in the rear, instead of cutting it out.
Indeed, but then it wouldn't be a proper Citroën.
It's what we love about French cars. Dare to be weird.
Right? I'd assume it would be terrible for aerodynamics too. Still, it does look pretty cool imo.