Car from the movie "Simone"

Remember that movie with Al Pacino and Rachel Roberts?

Just wondering if any of you car-savvies can tell me what sportscar Simone drove in the movie? It looks vintagey and Aston Martin-ish and has four headlights.
There's a shot of the convertible in this trailer:

http://www.apple.com/trailers/newline/simone.html

Please let me know if you are clued in!

Thanks in advance!

I saw an Alfa Romeo very briefly in the trailer, but I can't tell you what model or year.

I'm pretty sure that was a 1967 Alfa Romeo Sypder.

It's a Giulietta Spider 1962 I think.