What you are looking for (if I understand you right) is the keys of %array sorted by their values.

Try this (see the -values line):

popup_menu(-name=>"array",
    -values=>[sort {$array{$a} <=> $array{$b}} keys %array],
    -labels=>\%array,
    -default=>$array1,
    -class=>"formfield")
[download]

BTW, why did you name a hash "%array" ;-)?

Update: Here's a quick test:

use CGI qw/:standard/;

my %array = (a => 2, b=>1, c=>3);
print popup_menu(-name=>'test',
    -values=>[sort {$array{$a} <=> $array{$b}} keys %array],
    -labels=>\%array)

__END__
<select name="test">
<option  value="b">1</option>
<option  value="a">2</option>
<option  value="c">3</option>
</select>
[download]