The code looks correct. On a stylistic note, I would write it slightly differently.

my %cache;
sub first_line
{
    my ($filename) = @_;

    unless (exists $cache{$filename})
    {
        open( my $fh, $filename ) or die "Cannot open '$filename': $!\
+n";
        $cache{$filename} = <$fh>;
    }

    return $cache{$filename};
}
[download]

Instead of checking for the existence of the cached value, I check for the non-existence of the cached value. If it doesn't exist, I populate it. That way, I always return the cached value and the logic is slightly easier to work with.

On a sidenote, I would look at Memoize. It's a module that's built to do exactly what you're trying to do.

Update: Changed return to die as per jdporter's comment that reading an empty file gives back undef.