The lines you read from F1 go into $_ and not into $file. You check the wrong variable and/or you print the wrong error message.

I would rewrite your code as:

my $file = $_;
my @tags=(qw(ct sect1 sect2 sect3 sect4 sect5 sect6));
my %allowed_tag = map { $_ => 1 } @tags;
while (defined (my $line = <F1>)) {
    $line =~ /<([^>].+)>/
        or die "Couldn't extract a tag from >>$line<<";
    my $tag = $1;
    die "Incorrect entry >>$tag<< in >>$line<<"
        unless exists $allowed_tag{$tag};
    print "Found tag $tag";
};
[download]