Using the dir method of Net::FTP to get a directory listing, you can feed this into File::Listing to extract the desired information, as in the following example:

use strict;
use warnings;
use Net::FTP;
use File::Listing qw(parse_dir);
use POSIX qw(strftime);
my ($host, $user, $passwd) = ('a.b.org', 'me', 'pgrx%sf');
my $dir = '/some/dir';
my $ftp = Net::FTP->new($host)
    or die qq{Cannot connect to $host: $@};
$ftp->login($user, $passwd)
    or die qq{Cannot login: }, $ftp->message;
$ftp->cwd($dir) 
    or die qq{Cannot cwd to $dir: }, $ftp->message;
my $ls = $ftp->dir();
foreach my $entry (parse_dir($ls)) {
    my ($name, $type, $size, $mtime, $mode) = @$entry;
    next unless $type eq 'f';
    my $time_string = strftime "%Y-%m-%d %H:%M:%S", gmtime($mtime);
    print "File $name has an mtime of $time_string\n";
}
$ftp->quit;
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