Short answer: choose an AC company in spring, not in the August breakdown. Verify the state license, ask how they price diagnostics, favor companies that talk about fixing before replacing, and read reviews for how they behave in peak season.
Why it matters here. In Jacksonville the air conditioner is not a comfort, it is infrastructure. It runs most of the year, and when it fails in summer the house becomes unlivable in hours. Everyone eventually has an AC story; the goal is a boring one.
The license check. Florida licenses HVAC contractors at the state level. The number belongs on the website, the truck and the paperwork, and a company that hesitates when asked for it has answered your real question.
Repair-first is the tell. A trustworthy company explains what failed and what it costs to fix before it mentions replacement. If every visit somehow ends in a quote for a new system, keep looking.
Peak-season reviews are the honest ones. Anyone can be responsive in February. Read what customers say about July: response time, honored quotes, and whether the fix held.
Where to look. Jacksonville's AC and HVAC companies are listed under /directory/?cat=Home+Services in the /directory, with reviews from members on your side of town. Save one now; the hottest week of the year is not the time to start reading.