すまん、超基本ｗ

my %file = ();

{
    open my $fh, '<test.txt'    or die;
    $file{'fh'} = $fh;
}

my $line = <$file{'fh'}>;   # NG
print $line;

my $fh = $file{'fh'};
$line = <$fh>;  # これなら ok.
print $line;