Quantum fields in regions of extreme spacetime curvature give rise to a wealth of effects, like Hawking radiation at the horizon of black holes. While quantum field theory can only be studied theoretically in black holes, it can be tested in controlled laboratory experiments. Typically, a fluid accelerating from sub- to supersonic speed will create an effectively curved spacetime for the acoustic field, with an apparent horizon where the speed of the fluid equals the speed of sound. Here we create effective curved spacetimes with a quantum fluid of light, with smooth and steep acoustic horizons and various supersonic fluid speeds. We use a recently developed spectroscopy method to measure the spectrum of acoustic excitations on these spacetimes, thus observing negative energy modes in the supersonic regions. This demonstrates the potential of quantum fluids of light for the study of field theories on curved spacetimes.