Does Fizz target the spell to replay?

Yes, Fizz, Trickster targets the spell in your trash that you choose to play.

According to RiftJudge FAQ #6132 and FAQ #10020, you must target the specific spell in your trash at the moment you add Fizz's "When you play me" (WYPM) triggered ability to the chain.

Additionally, as clarified in RiftJudge FAQ #9320, when you play the spell from your trash during the resolution of Fizz's ability, you must declare any targets that spell requires at that time (following the normal rules for playing that spell).