I made a few additional changes reflecting the currently widely accepted good practices.

you missed one ;)

- open (my $F, $file) or die "cannot open file $!";
+ open (my $F), '<', $file or die "cannot open file $!";
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@OP: If for some reason you have a file '>123.txt', then open (my $F, $file) would open the file for writing and truncate it.

Two purely cosmetical changes would be to replace $F with $fh and also add the filename to the error message, like "cannot open file '$file': $!".

@OP: I would consider replacing 'die' with 'warn and next', so that you can process the remaining files even if one is not readable to the current user.

Variant a)

open (my $F), '<', $file
  or warn "cannot open file '$file': $!";
defined $F
  or next;
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Variant b)

open (my $F), '<', $file
  or warn "cannot open file '$file': $!" and next;
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I prefer Variant a) because chaining conditionals may lead to surprises. Mostly because 'or' short circuits the evaluation and due to operator precedence.