I assume you have ground named as GND in schematic, name gets to the netlist and you got GND net in pcbnew.
Place components where you like, add ground fill tied to the GND net.
I assume that at this point you are trying to run freerouter. You run it and import it back -> no ground paths at all.
This is the freerouter doing it. You need to manually route the ground path so kicad can see it meets DRC spec.
Freerouter assumes the groundplane is good enough and doesnt do actual path for the fill.
You can do it after importing the autorouted traces.
The people telling to rename the plane is way to get around it, but freerouter does vias to the groundplane so you just need to connect them using traces for the DRC (if design is loose enough, unlike in this case?)
By manually adding the traces for groundplane, you might need to modify existing traces.
If you try running freerouter after routing signals, deleting the fills to get the traces, it might fail where manually it would work.
DRC check on freerouter is little more strict by default than on kicad (actually checked this just now, router was stuck but manually it worked as freerouter didnt like the angle the trace was on pad).
Same applies if you use Vcc on top fill/whatever.
Just route it without planes, then afterwards add ground fill and manually put vias into it?
Hard to say without knowledge how crammed the design is.
If it still fails, kick/rotate the components around a bit.