I live in Florence, Ala., retired from TVA, and get to Huntsville and Birmingham pretty regularly, mostly for shooting events.
Alabama is a May Issue CCW state. The Sheriff has discretion on whether to issue a pistol permit and there are no statewide standards. Few will deny you, but writer Jan Stevenson said he knew of one that would, a good many years ago. An Alabama permit is good in adjoining states, Tenn., Miss., Ga., and Fla., but not a whole lot of other places because of that lack of statewide standards and "training."
Shooting sports in North Alabama depend on your interest and your willingness to travel a bit. I go to IDPA club shoots in Sheffield, Huntsville, Hartselle, Arab, and Birmingham; six to 130 miles. I will go a bit farther to sanctioned matches, add Memphis and Manchester, Tenn. I branch out a little with BPCR in Birmingham and Long Range in Tullahoma, Tenn.
There is also IPSC to be had, CAS, some NRA, and some Trap and Skeet.
A rifle shooting friend grumbles at the lack of full scale NRA ranges and events, and goes to Tullahoma whenever they shoot, as well as longer excursions for big matches.