I'm not a big fan of such big tables, so instead I'd propose this:

use 5.010;
use strict;
use warnings;
use utf8;
use Unicode::Normalize qw/NFKD/;

sub unaccent {
    my $s = NFKD shift;
    $s =~ s/\pM//g;
    return $s;
}

say unaccent "Les Misérables";
__END__
Output:
Les Miserables
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The NFD normalization form has the base character and the accent split into two different characters, and the substitution removes all the marks (\pM).

(And Unicode::Normalize is a core module since perl 5.8, and you really, really don't want to use anything older than that for Unicode stuff).

Thanks, I will try that. What is the 'shift' supposed to do in the code. I know what it does in general, but it was in the original code, and now here, and I don't quite see how it fits in.

shift without an argument obtains the first element of the argument list of the subroutine, so it fetches the string that is passed to the subroutine.

Perl 6 - the future is here, just unevenly distributed

1. Single quotes do not interpolate. Use $table{"$1"} or even no quotes at all: $table{$1}.
2. Tell Perl what encoding your script uses. It should be UTF-8 and you should therefore use utf8;.
3. If you are reading the data from a file, set the input encoding. You can use either

   open my $IN, '<:utf8', $filename or die $!;
   [download]

   or

   open my $IN, '<', $filename or die $!;
   binmode $IN, ':utf8';
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   Set the output encoding to UTF-8, too, if you plan to output any accented characters.

Hmmm, but I don't know what kind of input I'm getting. I have the 'guess' function running just before this part of the script to determine if I need to encode into UTF8 first or not. Will setting the input encoding to be UTF8 change the input into UTF8, or just tell the server to expect UTF8?

Also consider Text::Unidecode. It has the property of also transliterating Chinese characters. Whether that is wanted is a different question.

Depending on how your file is really encoded, the tr/// function might be much easier to use and probably faster. Something like this (to be completed):

$str =~ tr/âàäçéèêë/aaaceeee/;

There are a number of cases where this simple tr/// function works well. If not, well, then the Unicode modules described by others.

There is a last point, though, which I can see as a problem, and which is in fact the main reason why I am posting here. "Unaccenting" letters may be less trivial than you may think. In French, all letters with an accent can be "unaccented" by just taking the same letter without the accent, this is the common way of doing things that when accents are not available. But in German, ä is usually rendered by ae, ö by oe and ü by ue. Similarly, I would tend to believe that the Scandinavian or other languages which have an 'å' probably don't translate it into an 'a'. This is just a warning that, depending on what exactly you are trying to do, your contemplated solution might be a bit simplistic.

Update: crossed out the first paragraph following choroba's comment. I had misread the regex.

Are you planning to write a line like that for each of your accented letters?

Meditate about the substitution a bit more. Remember negative character classes. There is nothing more to be written.
لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ

Right, I looked at it too quickly and missed the point.

     Depending on how your file is really encoded, the tr/// function might be much easier to use and probably faster. Something like this (to be completed):

     $str =~ tr/âàäçéèêë/aaaceeee/;

I originally used the tr function like you suggested. Why it didn't work so well, I'm not sure. I had:

$_ =~ tr/àáâãäçèéêëìíîïñòóôõöùúûüý/aaaaaceeeeiiiinooooouuuuy/;
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but it produced a two character result, similar to the ?? in my original question above. However, the first output character was an 'a' regardless of what the result was supposed to be, and then an unprintable character placeholder which i can't duplicate here. Like the above code, it recognized which character to replace, but then didn't do it right.

Thanks for the tip on German/Scandanavian etc languages where they don't translate 1:1, although I'm not so worried about that, at least not at the moment. :)