Sorry, you can't glue it back up or else it will fall back down. Being in Florida doesn't help either.
You have to remove the headliner, scrape all the old stuff off, and buy some replacement headliner. They sell generic "mousefur" headliners in a variety of colors at parts stores or ebay. Then use contact cement on both clean surfaces and press it on. Good as new!
Or you could buy a used headliner from a junkyard.