The casquette - cycling cap - is styled to keep the sun out of your eyes and the rain off your face while not obstructing your vision.
While they were plenty available in the 80s, they're a bit harder to find in the U.S., and often come plastered with team names or advertisements. So, our vote, as per usual, is to make your own.
Flickr user Panda Face has created a pattern that allows you to use whatever sort of fabric you'd want.
"Here is a basic pattern for the cycling cap I made. I have a big head so pull in the seams untill it fits you, then hem the length and stich the bill on. Cut on the thick lines, sitch the thin. If you download full size and print at 72ppi it should come out near the correct scale."
Also, be sure to cruise the Flickr page for plenty of photos and fabric combos featuring this design.