Two articles above the article I was searching for in The Laws and General Ordinances of the City of New Orleans by Henry J. Leovy and C.H. Luzenberg, published in 1870, I discovered this:
Article 661. No person shall exhibit, or cause to be exhibited, in this city, any bull or bear fight, or pugilistic contest, or make any immoral exhibition, or form processions for the purpose of attending such exhibitions.
Incidentally, it appears that gator fighting was perfectly acceptable.