The Falcon eventually looked like this in its debut in the 1960 model year. As the September 1959 Motor Trend explains, Falcon (originally called XK Thunderbird, then Lavion, then Astrion) was originally conceived as a smaller, cheaper Thunderbird (after Thunderbird spread its wings and fins and grew into a personal luxury car).
Here the quad headlamps are very close to the 1958-1960 Thunderbird...
...while the rear profile design (top) is a bit like the 1960 Rambler. The rear design on the left would eventually find itself used (more or less) on the 1962 Mercury Comet. The design on the right, however, is like a finless 1958 Thunderbird.
As explained in the article, the Ford designers were very much in love with the vertical grille (above and below) which was of course, used on the ill-fated Edsel. Note the double-Cyclops stacked headlights on the European-like design below. Surely no one thought that would be approved.
A variation on rear end, above, right, would later turn up on the 1961 Thunderbird.
Aside from the quad headlights, this design for the grille was getting closer.
Curiously, Motor Trend tells us the top sketch on this page was rejected, but it's the closest to the design that made the final cut. The design at the bottom recalls the 1962 Mercury Meteor.