A fence will limit wall construction (wooden or stone) on any floor above it to only an arch.
With an arch and fence already built on ground level, all floors above can only have another arch built on that tile border, no other wall type options are available.
Presumably also the case (though untested) if the fence is already constructed on any floor it would block those above (and possible even below)
(Originally reported in game by Nyuna on Xanadu, but reproduced by myself to double check)