Your approach seems pretty reasonable. Just one pointer:

{
  local($/) = "...end of paragraph delimiter...";
  while (<F>) {
    my $line = process_paragraph($_);
    print OUT2 $line;
  }
}
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This localizes the value of $/ so that it gets reset upon leaving the block. It's a defensive measure so that you don't get surprised later on when you expect $/ to contain the default value.

Also, note that in the while loop, $_ will contain the end of paragraph delimiter. You can chomp it or just leave it, depending on what your processing routine does.