Others have suggested far better ways.

However, in light of your repeated notes that you really want only a mod to your existing sub:

#!/usr/bin/perl -w
use strict;
use 5.016;
# 1088912 

my @args=@ARGV;

find_string(@args);

# mod of OP's original:

sub find_string {
  my $file = shift;
  my $string = shift;
  open my $fh, '<', $file;
  while ( <$fh> ) {
      if ($_ =~ /\Q$string/) {
          warn "Test result is FAIL (i.e. $string is present in $file)
+";
      } else {
          if ($_ !~ /\Q$string/) { 
              say "\t Did NOT find $string in $_";
          }
      }
  }  

}
[download]

But your statement (" Most of my scripts use that function") and request that we give you a modification rather than a different approach puzzles me: I don't see why modifying your existing code in multiple scripts creates less workload than replacing it -- in the same number of scripts -- with something including the improvement for which you asked.