You could try escaping (as explained above) or you could use multiple here-doc strings, only some of which interpolate:

print <<"FOO_INTERP" . <<'FOO_NONINTERP';
    =head2 $fnName( )
FOO_INTERP

    =over 4

    =item Parameters:

    None

    =item Description:

            Display backup status.

    =item Returns:

            %{$outputParams{PAYLOAD}}; DFM Database related attributes
            $outputParams{TIMETAKEN}; Time taken to run a CLI at Serve
+r
            $outputParams{CMDSTATUS}; Status returned by the command e
+xecuted
            $outputParams{CMDOUTPUT}; Output returned by the command e
+xecuted


    =back

    =cut

    # ================================================================
+===========

FOO_NONINTERP
[download]

Or use printf:

printf <<'FOO', $fname;
    =head2 %s( )

    =over 4

    =item Parameters:

    None

    =item Description:

            Display backup status.

    =item Returns:

            %{$outputParams{PAYLOAD}}; DFM Database related attributes
            $outputParams{TIMETAKEN}; Time taken to run a CLI at Serve
+r
            $outputParams{CMDSTATUS}; Status returned by the command e
+xecuted
            $outputParams{CMDOUTPUT}; Output returned by the command e
+xecuted


    =back

    =cut

    # ================================================================
+===========

FOO
[download]