The default encoding of the output is 7bit which clearly can't display characters outside the 7bit ASCII. Use the 8bit encoding instead:

my $msg = MIME::Lite::TT::HTML->new(
          Encoding    => '8bit',
          # ...
[download]

Also, I don't see use utf8; anywhere in the source. If you're using UTF-8 in your source code, you should tell Perl about it.