<> is two different operators. Based on its operand, it's an alias for readline or it's an alias for glob. Here are two ways of forcing readline:
while (my $line = readline($FH[$i])) {
...
}
my $fh = $FH[$i];
while (my $line = <$fh>) {
...
}
There's still the question of why you are using global variables for no reason.
open(FILE_A,">","a.txt") || ...;
open(FILE_B,">","b.txt") || ...;
my @FH=(*FILE_A,*FILE_B);
should be
open(my $FILE_A,">","a.txt") || ...;
open(my $FILE_B,">","b.txt") || ...;
my @FH=($FILE_A,$FILE_B);
You're using 3-arg open which was introduced at the same time as lexical file handles, so it's not a backwards compatibility issue.