This trail area is pretty good for birding, but grab your binoculars and your camera and try wandering off the main trail, both to the north of the trail (across the little footbridge), and south of the main trail area.
There are four major North American flyways: the Atlantic the Mississippi, the Central and the Pacific. Fort De Soto park on the Florida west coast is a key point on the Atlantic Flyway.
In fact, if you want to learn more, you might want to read about Great Florida Birding Trail. Florida Fish and Wildlife Conservation Commission has designated 445 birding sites throughout Florida. Fort De Soto Park is one of the nine special "gateway" sites because of the exceptional birdwatching that the park offers.
You can download and print out their excellent birding trail guides. Here's the one that includes Fort De Soto Park.