In what encoding is it now? Suppose it's in encoding $x, try this:

use Encode qw(from_to);
my $str = do { local(*ARGV); @ARGV=$File; <> };
open my $out, '>', 'X:\TestData.txt.UTF-8' or die $!;
print $out from_to($str, $x, 'UTF-8');
close $out or die $!;
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Of course you can also just use IO layers.

open my $in, "<:encoding($x)", $filename or die $!;
open my $out, ">:encoding(UTF-8)", "$filename.utf8" or die $!;
select $out;
pirnt  while (<$in>);
close $in or die $!
close $out or die $!;
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Your version can't work because Encode::encode doesn't modify its arguments, and you're ignoring the return value of the map.

(Update: fixed typo in from_to, ambrus++)