Any islands that are overlapping the ground traces will be connected but show as not connected.
You said Copper fill and I just want to confirm you actually clicked ground fill not copper fill as copper fill will never connect to anything.
You only need to select one single pad or via that is part of the ground fill net. Fritzing follows that path and makes all the connected pads part of the ground fill.
Also note that ground fill will only be connected by small little tabs to the pads and holes. This is to make it possible to solder because if it was just solid the large copper area would take heat away fro the pad too quickly making the solder joint weak.
If none of this helped maybe upload a picture of a board after running ground fill.