I haven't been able to find any reliable etymologies online for the folkloric Freischützen (or the Freikugeln they use), and specifically why it contains the word Frei ('free').
The closest I've found was Friedrich Kind, who suggested it might be related to Freikorps ('free-corps'; independent regiments), whose infantrymen were called Freijäger ('free-hunters'). But apparently the Freikorps were first created almost two centuries after the phrase Freischütz was used about these magic marksmen (1759 vs 1586). He also mentions French francs-archers ('free archers'), which is plausible (they were created in 1448), but he doesn't give any evidence that it was related to the folklore in any way, let alone how or why they would be connected.
The KLUGE article for Heckenschütze mentions Freischütz as a literal translation of the French franc-tireur, but again the francs-tireur seem to be much later than the Freischütz folklore (1870s, with the earliest use of the phrase in Gallica being 1788).