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...
open my $fh, ">:utf8", "accentTestOutPut.xml" or die $!;
...
$doc->printToFileHandle($fh);
# or
$doc->print($fh);

$ hexdump -C accentTestOutPut.xml 
00000000  3c 3f 78 6d 6c 20 76 65  72 73 69 6f 6e 3d 22 31  |<?xml ver
+sion="1|
...
00000020  46 2d 38 22 3f 3e 0a 3c  54 45 53 54 3e 20 c3 a9  |F-8"?>.<T
+EST> ..|
00000030  20 3c 2f 54 45 53 54 3e  0a                       | </TEST>.
+|
                                                     ^^^^^

sub printToFile
{
...
    $self->print ($fh);
    $fh->close;
}