We were there last month, and I recall seeing people fishing from the campground. You can also keep kayaks at your site and launch from there.
There is a watersports concession in the park with bait for sale, kayak and bike rentals - google water sports rental Ft. DeSoto and you'll find it. They have a store inside the campground just past the entrance.
It's a big park. The campground has a sea wall around it and it is not a swim area. You drive or bike to swim from the beautiful sand beach on the Gulf of Mexico. I think there is a fishing pier over there, too. There are boat trips to an offshore island.
The kids will probably enjoy the old fort with cells and places to climb up. There's also an old Quartermaster Museum. You can see some interesting wading birds, often strolling through your own site.
You know your children best - I would have loved it as a kid just for the beach alone, but there aren't game arcades, movies, amusement park rides, etc. there or close by.