There is a designated Cat launching ramp at Jacksonville Beach located at 8th Ave N. in , just about 4 blocks north of the new pier. It is not a boat launching ramp, but an old concrete ramp that allows you access to the beach so you can back your boat to the sand and cattrax it from there to the surf. You can't drive a car on the beach but you can back your boat onto it. There is car and limited trailer parking there.
I think it is the only place to launch at the beach but it's a good one and close to the action, i.e. restaurants, bars, music & sailorettes.
There is a fleet that sails out of the Rudder Club on the west side of Jax. It's located at the western side of the Buchmann Bridge crossing the St. Johns River. It's located in a very wide spot in the river and the sailing is great and the club is fun, as I was a member about 25 years ago.
If you're planning to sail around the Jacksonville University area you better pick your day carefully with all the current around there. You might inadvertantly find an alternate way to get to the beach with the outgoing tide.