I've successfully used:

open FH, $file_name or die "could not open $file_name: $!\n";
binmode FH, ":encoding(UTF-16)";
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though I'd also point out that it's not recommended to use bare filehandles anymore. However, I'm not sure if not using the binmode function is actually your problem, since you don't describe your error. What I saw before using the binmode was the file would appear broken -- instead of "this\tis\tthe\file" (in a tab-delimited file), I'd see "t h i s i s t h e f i l e" (or something close to that).