The reason for you not getting recursive answers (which you want in a case like this, where a CNAME points at a CNAME that points at an A) is printed in your answer:
;; WARNING: recursion requested but not available
That means, the nameserver you are asking (ns5.laposte.net) is an authoritative nameserver, not a recursive one (also know as a resolver). It will only look into its database and see if there is a record of the type you are looking for, In your case, it looks for an A record for conversation.ees.labanquepostale.fr, which doesn't exist. When explicitly setting the record type to CNAME you get the answer you expect, but nothing more (ie. the CNAME isn't followed). If you check on a recursive nameserver, dig will get recursive results until the A record is found:
; <<>> DiG 9.18.0 <<>> conversation.ees.labanquepostale.fr
;; global options: +cmd
;; Got answer:
;; ->>HEADER<<- opcode: QUERY, status: NOERROR, id: 24724
;; flags: qr rd ra; QUERY: 1, ANSWER: 3, AUTHORITY: 0, ADDITIONAL: 1
;; OPT PSEUDOSECTION:
; EDNS: version: 0, flags:; udp: 4000
;; QUESTION SECTION:
;conversation.ees.labanquepostale.fr. IN A
;; ANSWER SECTION:
conversation.ees.labanquepostale.fr. 299 IN CNAME prod-lbpee.web-application-front-customer.as8677.net.
prod-lbpee.web-application-front-customer.as8677.net. 299 IN CNAME prd-lbpee.web-application-front-customer-as.lbp-mail.as8677.net.
prd-lbpee.web-application-front-customer-as.lbp-mail.as8677.net. 2670 IN A 160.92.71.152