Life on earth is based on a salt-water metabolism: we all carry around salt-water inside us to bathe our cells which evolved to expect that environment. So, with only fresh water, evolution would have had to happen in a completely different way: basically you're looking at rewinding the clock 4 billion years and seeing what happens without sodium and or chloride. My suspicion is that the various chemical processes which are running all the time in our cells could be done differently, with different elements, and you would get life which was broadly similar to the life we know, until you got down to the level of biochemistry. However, maybe the dependence on the alternative chemicals would push life in a completely different direction.
Basically you're looking at a total reboot of evolution, from the bottom up, and it's quite tricky to speculate what you're going to end up with after that.
EDIT - i forgot to think about weather and geology. I'm not particularly knowledgable about meteorology, geography and geology, but my guess would be thus:
The current state of the earth's physical geography is due to three main processes: rock formation, plate tectonics and weather. The rocks are formed, smashed together/pulled apart on the big scale by tectonics to make mountain ranges and valleys, and then weather erodes the rocks. In addition to this, tectonics and perhaps other geophysical processes move landmasses under and above sea level over huge time scales, so you have land that used to be on the sea bed now forming the earth's walkable surface, etc.
Since water evaporating from the sea doesn't take the salt with it anyway, the weather wouldn't be very different. In other words, i don't think that the oceans' salt content plays much part in the Earth's weather, because i don't think there's much salt in the atmosphere. I doubt that the salt content of the rocks plays much part in tectonics either. So, the only remaining aspect of the earth's surface which could be affected by the removal of sodium and/or chlorine would be the actual rock formation: perhaps we would have different kinds of rocks - in particular, we might have a smaller range of crystalline rocks in existence. But, i suspect we would still see the same broad processes, wherein tectonics and volcanoes make mountains, and the weather smoothes them out again, etc, and you have things like topsoil and silt and other "stuff" which change our planet's land surface from a bare rocky landscape into a softer "earthy" terrain which can support plants etc.