The Late Middle Ages are set within the time span of 1307-1485. It precedes the Renaissance, although signs of it were starting to manifest in the arts, including fashion, during this time period.
When it comes to female attire (upper-class, noblewomen), the most salient trait is the headgear. At this point in time the hats worn by females consisted on big and extravagant turbans , some round and some pointed, mainly worn by married and adult women. This was a way to separate them from the younger or unmarried girls who would wear their hair lose with hats that were much smaller.
Belts and clasps evolved remarkably as well, for it seemed to be the fashion to clasp tunics made of velvet and other rich fabrics that were quite thick. Therefore the wealthier you were the most sturdy and flamboyant the clasp. The tunics that the clasp would bring together the tunic to an ankle-length cloak. At this point the tunics and cloaks displayed a wide range of colors since more experimentation was made with mixtures and natural staining. Another fashion at the time (again, for noblewomen or females of genteel birth) was the long, flowing dress with no belt, tight at the waist line and low at the breast line. This was lined with fur and had fitted sleeves.
Males would wear shorter tunics. In France there was also a tendency to display the family crest somewhere in the wardrobe. A very famous piece of male clothing was the houppelande. It consisted on a high collar under which fur lining would be displayed prominently. Headgear was also common however it in no way compared to that of females in terms of size and extravagance. Most male headgear was related to their line of work. Court Jesters shown traditionally in middle age reproductions got actually had the hats we see in plays and movies. This is how distinctly males identified themselves.
Men also had a tendency to wear "false shoulders" to appear broader. These were worn underneath their short tunics. In contrast, however, priests were expected to relinquish any accent of fashion and were subdued to wear an alb, or long tunic. This was also evident in lawyers and justices who also wore a black cap to distinguish themselves. Priests also wore their hair in tonsures and covered their heads with a cap.
All shoes of this period were mainly slippers covered in silk and sandals. The interesting fact is that priests could not wear shoes during ceremonies and were resorted to wear their sandals only outside of church. More information can be found in Albert Racinet's Illustrated History of European Costume published in English in the year 2000, and extracted from Racinet's Le Costume Historique.