It seems the printToFile method has not been written with unicode in mind¹... but you could create a properly UTF-8-encoding file handle yourself, and then either use ->printToFileHandle, or simply ->print

...
open my $fh, ">:utf8", "accentTestOutPut.xml" or die $!;

# Print doc file
$doc->printToFileHandle($fh);
# or
$doc->print($fh);
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$ 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|
00000010  2e 30 22 20 65 6e 63 6f  64 69 6e 67 3d 22 55 54  |.0" encod
+ing="UT|
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>.
+|
                                                     ^^^^^
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___

¹ current implementation:

sub printToFile
{
    my ($self, $fileName) = @_;
    my $fh = new FileHandle ($fileName, "w") ||
        croak "printToFile - can't open output file $fileName";

    $self->print ($fh);
    $fh->close;
}
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