Apex domains cannot have CNAME records.
Question and response
Question
dig d340j3r5r7spbj.cloudfront.net. NS
Answer
d340j3r5r7spbj.cloudfront.net. 5 NS ns-668.awsdns-19.net.
d340j3r5r7spbj.cloudfront.net. 5 NS ns-1626.awsdns-11.co.uk.
d340j3r5r7spbj.cloudfront.net. 5 NS ns-391.awsdns-48.com.
d340j3r5r7spbj.cloudfront.net. 5 NS ns-1122.awsdns-12.org.
Authority
The response has no authority records.
Additional
. 0 OPT ; payload 1232, xrcode 0, version 0, flags 0