How about:

use warnings;
use strict;

print sort {
    my @a = ($a =~ /(\d*)_FFF(\d*)_(\d*)/);
    my @b = ($b =~ /(\d*)_FFF(\d*)_(\d*)/);

    my $i=0;
    for ($i=0; $i < $#a && $a[$i] == $b[$i]; $i++){}
    $a[$i] <=> $b[$i];
} <DATA>;

__DATA__
0011_FFF0_0010
00111_FFF00_00011
000_FFF0_0000
[download]

Gives:

$ perl /tmp/tst.pl 
000_FFF0_0000
0011_FFF0_0010
00111_FFF00_00011
[download]

Not exactly exhaustive, but I submit it makes a not unreasonable basis for experimentation...

Update:

...which is a variant on the solution with which ikegami beat me to the draw:-)