No, Your code is working for me without removing the second loop.

use strict;
use warnings;

open(file_one,"<","ABC")or die $!;
while(my $line = <file_one>)
{
        open(file_two,"<","CDE") or die $!;
                while(my $line2=<file_two>)
                {
                        print "line : $line  line2 : $line2 \n";
                }
                close(file_two);
}
[download]

line : test
line2 : CDE

line : test
line2 : CDEEE

line : test
line2 : CDEEEE

line : test121212121
line2 : CDE

line : test121212121
line2 : CDEEE

line : test121212121
line2 : CDEEEE

line : adskjdsadjdka
line2 : CDE

line : adskjdsadjdka
line2 : CDEEE

line : adskjdsadjdka
line2 : CDEEEE

Update:

Added file content.

ABC:

test
test121212121
adskjdsadjdka

CDE:

CDE
CDEEE
CDEEEE