The problem is you aren't 'print'ing to the file anywhere.

The Perl Cookbook p.243-244 recipe 7.10 shows "Modifying a File in Place with -i Switch" - you basically open the file with "+<", read the whole file into an array, update the array, then rewrite the file and truncate it to its current seek pointer:

   open(FH, "+< FILE") or die "Opening: $!";
   @ARRAY = <FH>;
   # change ARRAY here
   seek(FH,0,0)           or die "Seeking: $!";
   print FH @ARRAY        or die "Printing: $!";
   truncate(FH,tell(FH))  or die "Truncating: $!";
   close(FH)              or die "Closing: $!";
[download]

If you don't mind using a temporary file, there's another recipe in the same section.

HTH.