I think you are going to have to come up with something, the light fixture you show is pretty specialized and my Google-Fu is coming up empty for any type of base for existing lights that house a receptacle.

Getting anything to look decent is going to be a challenge. I once had to do this and managed to fish a wire from the lights box down to a hole in the wall and mounted a weatherproof box externally to the wall. It looks better than running a conduit down the outside, you can run a conduit provided you can come up with some sort of extender ring that's weather proof and has openings for conduit.

As far as GFCI, depending on how you go you can either do as u/dave729us says and protect the entire circuit with a GFCI breaker, or if you manage to drop a wire or conduit, just use a GFCI recep in the external box.