So something like a fish is definitely out the question, because the period when Mars was habitable was only like 500-1000 million years after the solar system formed. Complex life like simple animals (jellyfish,sponges) didn't evolve until 3700 million years into Earth's history and fish didn't evolve until 4100 million years into Earth's history. Mars never had the time to evolve something so complex as a fish.

So instead of fish we're looking for much simpler microbial life. An individual fossil microbe is far too small for the rover to spot. Fortunately though, even simple microbes can group into larger colonies leaving behind rock structures called stromatolites which are really distinctive and are known from rocks of similar age on Earth. So that's the kind of thing we're hoping the rover just stumbles on.

It's worth adding though that Curiosity has been exploring lake-bottom sediments for 10 years now and nothing remotely like a stromatolite has yet been found. Perhaps that's telling us something. Maybe there were microbes but they didn't form into colonies for some reason, maybe the water conditions were wrong. Maybe there was life on Mars but it never reached this lake. Or maybe there was no life at all. OOOOor maybe there are stromatolites in Gale Crater and we just landed in the wrong place ;)