One way that won't break depending on the encoding of your source (.pl) file is:

use HTML::Entities qw( decode_entities );

# It is technically possible for Uuml to
# be encountered in French, but I don't
# know of any words that use it.
my @french_accents = map decode_entities("&$_;"),
                     map +($_, lc),
                     qw( Acirc  Agrave
                         Eacute Ecirc  Egrave Euml
                         Icirc  Iuml
                         Ocirc
                         Ugrave Uuml
                         Ccedil
                         AElig  OElig
                      );

my $french_accents = join '', @french_accents;

$form_values{$field} =~ /[^A-Za-z0-9_'-\.\s$french_accents]/) {
[download]

Tested.

Note: Don't forget to decode the value placed in $form_values{$field}.

Update: Added Ocirc. Should Ucirc be on that list? It's been so long since I've written in French.