One thing I do not understand is that it looks as if you are looping through the file, but match against a constant $string.

Also you should be using

use strict;
use warnings;
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In your code there is one thing (if I read it right): Your variable $string starts with an opening parenthesis, but you anchor your match to start without it.
You also have additional blanks around your \s+ matches. You would require 3 blanks to match: one literal one, then one from \s+ and then another literal one. In your string you only have one.

So either change (added quotes around the $string assignment, updated m//) code to

# string to be searched 
my $string = '(FT CDS complement(join(18028..18116,19351..20668)))'; 

#search for the first line highlighted in bold 
if ($string =~ m/^\(FT\s+CDS\s+complement\(join\([0-9.,]+\)\)\)$/) { 
    print 'match' 
} else { 
    print 'no match' 
}
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cheers, si_lence