In period writing I have seen Fusil, Fuzil, Fuzee, Fusee and Fuke. So far I have not seen Fook so that makes me think it was corrupted to Fu-kee not Fuke as in Luke.
Do you know what a fusil is?
It's a light musket.
Briefly in the 17th Century it may have referred to all the early flintlock muskets. At that time the flintlock was new technology and somewhat lighter or at least handier than the matchlocks of the regular infantry. The troops issued these new arms guarded artillery and the baggage. These troops were light, I guess you could consider them light infantry and they eventually became known as Fusileers.
By the 18h Century trade fusils were produced by the Dutch, French and English. These light muskets transformed the Native Americans from a near stone age culture into a gun culture.
The fusil was the precursor to the American Longrifle, if not entirely by form but by function and use. Basically a long rifle is simply a fusil with a rifled bore for the most part.
