Assuming the "simplified" example isn't excessively simplified...
My thinking would be to effectively go through each file, then if it exists in A:\A\, copy it to A:\A, and if it exists in A:\N, copy it to A:\N
Under MS-DOS I think this requires two batch files. One to go through the actual files, and the second which accepts each file and copies it to the appropriate folder.
There is, of course, a caveat here, in that it will copy and overwrite files regardless of changes. This is intended to be run while E:\ is the current directory.
copydirs.bat:
for %%F in (*.*) do checkflp.bat %%F
checkflp.bat:
for %%D in (A N) do if exist A:\%%D\%1 copy %1 A:\%%D\%1 /y
regarding the caveat, it is possible to expand this to only copy files that were changed. This cannot readily be done with COPY or XCOPY; however, and it also adds in a different limitation.
MS-DOS has a file comparison tool, FC, which can compare files. However, it does not present an errorlevel to test.
However, the output of FC will differ, so it is actually possible to get an errorlevel if the files differ by piping the output of fc to find, since find will return an errorlevel. If we change checkflp.bat to, instead of copying directly, run yet another batch file to chain things off:
for %%D in (A N) do if exist A:\%%D\%1 copydiff.bat %1 A:\%%D\%1
and then create copydiff.bat:
fc %1 %2 | find "***">NUL
IF ERRORLEVEL 1 COPY %1 %2 /Y
FIND will give an errorlevel of 1 if it finds the specified text, so we use that to search the output of FC, which will only have *** if it found matches (otherwise it just says "FC:No differences encountered"). Then we can check said errorlevel to determine whether a file should be copied.
The limitation here is that it means that the Floppy Drive must have each f ile to be copied; if E:\ receives new files, those will NOT be copied. This also presumes these files are all in the root directory (Again, could be the downfall of the simplification, as others have pointed out).
I've not tested the above, either; so take appropriate precautions if testing/checking it!