What voltage is the coil? I would highly recommend using a 12V coil, you don’t want to apply 120V to the float, even if its rated for that I rather not have it that close to the water. You need to run a transformer in series with th coil and the float.
For the electrical, always interrupt (switch) the hot, never the nuteral. If your relay is DPDT you can do both but never just the nuteral.
You have to figure if your float is set to NO or NC most floats can be changed by removing the circlip and flipping the float mage net upside down. If your float is set to NO than you want to connect the hot wires to COM and NO, this is the way I would reccomend as the coil is only energized when the water level is down.
HTH
FWIW, I have one already wired just plug in wall, clip on floats and plug in the pump. PM me $20 shipped.