Tell us about yourself!
And yes, as long as the fluoride component is less volatile than water it will in effect remove the fluoride. It will also remove chloride, but less easily chlorine. Anything you can smell coming from the water you start out with, may end up to some degree in the distilled product.
Your thought is quite interesting and along those lines in science some components can be purified and concentrated using crystallisation. Ice crystals are indeed pure water, and whatever was initially dissolved or suspended in the water, will be concentrated outside the pure water crystals. So, if the pure crystals could be collected that would be an excellent source of pure water, but once you melt your ice, it will again have all the solutes and solids in it.
The benefits of fluoride seem to be questioned. Fluoride components are considered a health hazard.