I would use Perl. Any version newer that 5.0x has the necessary Net::FTP module.
#!/usr/bin/perl
use Net::FTP;
$ftp = Net::FTP->new("MACHINE_NAME", Debug => 0)
or die "Cannot connect to some.host.name: $@";
$ftp->login("USER_NAME",'PASSWORD')
or die "Cannot login ", $ftp->message;
$ftp->cwd("/pub")
or die "Cannot change working directory ", $ftp->message;
$ftp->get("that_file.tar.gz")
or die "get failed ", $ftp->message;
$ftp->quit;
You could then stuff this into the user cron. Hard coding the username and password does present obvious security issues. If you're interested in Perl, check out cpan.org and perlmonks.org
http://search.cpan.org/~gbarr/libnet-1.19/Net/FTP.pm