The derivation of Frank from a weapon can be questioned. The alternative etymology (supported by Grimms Deutsches Wörterbuch) is a derivation from the Germanic word Frank "free" (related to English frank "outspoken").
Not a short name for Francis or Francois, it stands on its own and is much older. Solid, forthright, noble, germanic derived name from the tribes of Frankenland, Frankfurt etc., the ford in the river where the Frankish people traded and crossed, English Franconia so latinized, = freedom free, exemption, right, privilege, thus the anglo saxon meaning of Candid lent the name to the western part of the merovengian empire, after the fall of roman Gaul, modern France. Ultimately from the shape of the spear head, their signature weapon noted by the romans. I bear it proudly.
The tribe of the Franks as mentioned did not only settle in what is called France / Netherlands (this was West Franken) but also in nowadays southern Germany (this was Ost [= East] Franken).There is still a German region called Franken with its regional capital city of Nuremberg. The Franks of today do not like to be called Bavarians, even if they live in the federal state of Bavaria.