Final answer:
The birthplace of jazz in New Orleans is known as Storyville, distinct from the French Quarter, which is characterized by Spanish architectural influences. The 'red-light' area of New Orleans where jazz was born is Storyville (C).
Step-by-step explanation:
The "red-light" area of New Orleans where jazz was born is C. Storyville. This district, established in 1897 and operational until 1917, was known for its jazz clubs where musicians like Louis Armstrong honed their craft. Although often confused with the French Quarter, famously known as Vieux Carré, which was redeveloped according to Spanish tastes with features like wrought-iron gallery porches during the period of Spanish rule, Storyville is indeed the correct answer.