The dot must go somewhere (the file name or the suffix), so you can roundtrip the original path back with

join $req_file, $dir, $ext
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As the documentation says:

You are guaranteed that $dirs . $filename . $suffix will denote the same location as the original $path.

If you want to remove the dot, you don't need to know the length of the string:

#! /usr/bin/perl
use warnings;
use strict;

use File::Basename;

for my $row('./filename.ext', '../filename', 'filename.s1.s2') {
    my ($filename, $dirs, $suffix) = fileparse($row, qr/\..*/);
    substr $suffix, 0, 1, q();  #  Remove the dot.
    print "$_\t" for $filename, $dirs, $suffix;
    print "\n";
}
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Update: Fixed to handle various suffixes. Change the regex to qr/\.[^.]*/ if you only want s2 as the suffix of filename.s1.s2.