I want to point out that the system that HEMA teaches (all though done usually by teaching longsword first) is a multi-weapon + unarmed system. A given technique that you can do with a longsword can also be done with a pole-axe. A pole-axe us better suited for armored combat (Harnischfechten) and a sword is better suited for unarmored combat (Blossfechten).

Although its worth pointing out, there are Harnischfechten techniques for longsword commonly referred to as half-swording (and you almost NEVER see these in movies). Btw, the unarmed component is called Ringen.

P.S. There are two similar schools for HEMA, the German and Italian school, my terms used above are the German terms. Most of the difference is either style, terminology or quite subtle.