This is already possible in Fritzing albeit a little complicated.
- Remove all existing copper fill.
- Clear all ground fill seeds.
- Use the view from above/below button to view it from the side you want as ground.
- Use the top layer/both/bottom layer button to only allow work on the ground side.
- Set your ground seed.
- Ground fill top/bottom which ever side you are working on.
- Clear ground fill seeds.
- Switch view to the opposite side.
- Switch the top/both/bottom to the opposite side.
- Set the ground fill seed but this time select your vcc instead of ground
- Ground fill top/bottom which ever side you are working on.
- Clear ground fill seeds just to be safe so you can’t accidentally click ground fill.
Now you will have 2 filled side with different seed points.