If you run this SSCCE then you see where one problem is

#!perl
use strict;
my $map = {
  one  =>1, two  =>2, three=>3,
};

my ($regex) = map {qr /\b(?:$_)\b/ } join '|', map {quotemeta} keys %$
+map;
change_file('test.txt',$map,$regex);

sub change_file {
    my ( $fn, $map, $regex ) = @_;
   # print $fn;

    open ( my $fh, '<', $fn ) or die "Could not open file '$fn': $!";
    my $str = do { local $/; <$fh> };
    print $str;
    close $fh;
    my $num_replacements = $str =~ s/($regex)/$map->{$1}/ge;

    if ( $num_replacements ) {
        write_new_file( $fn, \$str );
    }
}

sub write_new_file {
    my ( $fn, $str ) = @_;

    open ( my $fh, '>', $fn ) or die "Could not open file '$fn': $!";
    print $fh $str; #<-- error here should be $$str
    close $fh;
}
<
#test.txt
__DATA__
one two
three four 
five
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