Ok form what I figure you have several lines in F1 and you what to skip the first corresponding line in F2.

 
use warnings;
use strict; 

open( F1, "subsettest.txt" ) or die "file1: $!";
open( F2, "subsettest1.txt" ) or die "file2: $!";
my @s2s = ();
while ( my $s1 = <F1> ) {
   my $s2 = <F2>;
   if ( $s1 =~ /^>/ ) {
      foreach (@s2s) {print $_;}
      print $s1;
      @s2s = ();
   } else {
      push (@s2s,$s2);
      print $s1;  
   }
}
foreach (@s2s) {print $_;}
close F1;
close F2;
exit;
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