ISO 3200 is already pretty high. A tripod and long exposure, maybe with some panning (remember to start panning before you start exposure and keep following even after its done). Whether you sacrifice iso or shutter depends on how steady your hands are
But I think some more noise is better than shaked/blurry images.
Also, you don't have to use the auto exposure because the camera will try to make it "daylight bright" which will be impossible for moving subjects. You should probably dial in -2 or -3EV, or even try one of the auto SCN modes (There are a couple night-specific ones).
Beyond that, you can try using a flash (diffused, low power so it doesn't overpower the ornaments and blind people) or take photos of the parade as it passes a street light. You will have to take the first few shots to experiment and then commit to the thing you think is working best.