When I found that car, I immediately compared it with the barchetta by Frua.
My source (an article about this coachbuilder in a magazine) reports a different Coachbuilder and designer, but now that I found a couple of period pics of the Frua-bodied one, they indeed look the same.
The article (not only the caption) reports that "he worked on Lancia and Fiat chassis, realizing bodies that, in the Concorso d'Eleganza in XXXXXX and XXXX, won the 2nd prize. In these occasions he showed two prototipes, always designed by XXXXx, one based on a Lancia Aprilia chassis and another on a Fiat 1100 one. One picture shows an elegant 1100 S Spider" and the caption reads "The 1100 designed by XXXXX, 2nd at the Concorso d'Eleganza in XXXXX."
I do not trust that magazine 100 %, but the Coachbuilder is pretty obscure and all the pictures there (and info) came from its archive...