use List::AllUtils qw(first);
first { $_ gt "\xff" } split //, $string_of_characters

if ($str !~ /^[\x{00}-\x{ff}]*$/) {
        say "JA";
}
else {
        say "NEIN";
}

Benchmark: timing 10000 iterations of daxim, gwen , muffi,...
     daxim: 14.6732 wallclock secs (14.41 usr +  0.18 sys = 14.59 CPU) @ 685.40/s (n=10000)
     gwen : 0.830139 wallclock secs ( 0.82 usr +  0.00 sys =  0.82 CPU) @ 12195.12/s (n=10000)
     muffi: 0.690399 wallclock secs ( 0.68 usr +  0.00 sys =  0.68 CPU) @ 14705.88/s (n=10000)

use 5.020;
use List::AllUtils qw(first);
use Encode;
use utf8;
use Benchmark ':hireswallclock';

sub daxim {
    my $string_of_characters = shift;
    first { $_ gt "\xff" } split //, $string_of_characters;
}

sub muffi {
    my $str = shift;
    $str !~ /^[\x{00}-\x{ff}]*$/;
}

sub GwenDragon {
    my $string = shift;
    scalar grep /[^\0-\x{ff}]/, $string;
}

my $string = 'a' x 10000 . '€';

say "daxim:      ", encode('UTF-8',daxim($string));
say "muffi:      ", muffi($string);
say "GwenDragon: ", GwenDragon($string);


timethese(10000,
          {'daxim' => sub { daxim($string) },
           'muffi' => sub { muffi($string) },
           'gwen ' => sub { GwenDragon($string) },
          },
         );

#!/usr/bin/perl

use warnings;
use strict;

use Inline 'C';

my $text = "ASCII-Wort";
my $umlaute = "Ölmüller";
my $euro = "\N{EURO SIGN}";

print checkBeyondOrd($text) . "\n";
print checkBeyondOrd($umlaute) . "\n";
print checkBeyondOrd($euro) . "\n";
 
__END__
__C__
 
int checkBeyondOrd(char *a) {
    while (*a != 0) {
        if (*a < 0) {
            return 1;
        }
        a++;
    }
    return 0;
}