Can you fish there

There are no bodies of fishable waters there

Yes, there are multiple spots along the bank of Bayou Fountain where people regularly fish. The best spots are probably the ones along the tree line at the edge of the ball fields, and sometimes people even venture along the Semita Major trail on the downstream end of the fields, i.e. in the conservation area behind the observatory. If the bayou is high enough that day, you can also fish from the deck by the paddle launch, but if the bayou is low, there is often muddy land below. Walking around to the opposite side of the paddle launch inlet seems popular. (Or if you have a canoe or kayak, the bayou awaits.) There are plenty of trash cans at the launch and along all the parking areas, so there's always a place to properly dispose of any trash you make or just helpfully pick up. (Oh, and of course, if you're fishing, be sure to have your fishing license. I've seen Wildlife and Fisheries drop by to check.)