You could sort using a routine to decompose the accented letter to their base characters. Something like this perhaps.

sub deaccent {
    my $phrase = shift;
    return $phrase unless ( $phrase =~ y/\xC0-\xFF// ); #short circuit
+ if no upper chars
    # translterate what we can (for speed)
    $phrase =~ tr/ÀÁÂÃÄÅàáâãäåÇçÈÉÊËèéêëÌÍÎÏìíîïÒÓÔÕÖØòóôõöøÑñÙÚÛÜùúûü
+Ýÿý/AAAAAAaaaaaaCcEEEEeeeeIIIIiiiiOOOOOOooooooNnUUUUuuuuYyy/;
    # and substitute the rest
    my %trans = qw(Æ AE æ ae Þ TH þ th Ð TH ð th ß ss);
    $phrase =~ s/([ÆæÞþÐðß])/$trans{$1}/g;
    return $phrase;
}
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used as:

foreach my $row_db ( sort { deaccent($a) cmp deaccent($b) } @$selected
+ ) {
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foreach my $row_db ( sort { deaccent($a->[1]) cmp deaccent($b->[1]) } 
+@$selected ) {
  my ($ID, $column1, $column2) = @$row_db;
  print "$column1\n";
}
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Or as a Schwartzian Transform. (probably not worth it unless @$selected is large)

foreach my $row_db (map { $_->[0] } sort { $a->[1] cmp $b->[1] } map {
+ [$_, deaccent($_)] } @$selected ) {
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foreach my $row_db (map { $_->[0] } sort { $a->[1] cmp $b->[1] } map {
+ [$_, deaccent($_->[1])] } @$selected ) {
  my ($ID, $column1, $column2) = @$row_db;
  print "$column1\n";
}
[download]

Note: this only covers ISO-Latin-1, if you need other code pages, modify deaccent() to suit (or possibly use Text::Unidecode)

UPDATE: fixed errors.