Here is a good reading about double routers setup.
(Important: I didn't mention that my ISP router doesn't have a built-in "bridge mode".)
I've finally decided to test the "weak" firewall configuration of the Livebox. Turning the DMZ On again allows me to delete all port forwarding rules set in the front router, which is what I aim for (simplicity + flexibility). Cool 
So far everything is working OK, and my NAS is accessible from the Internet. Plus no more NAT loopback issue like I had in the past! (Is it because IPv6 is setup correctly from a LAN point of view? If I ping v4 my NAS from its domain name, it fails... but ping v6 works.)
Questions:
- Will the TV decoder be exposed to some threats? I don't know if it has its own firewall.
- Am I effectively in a "double NAT" setup? How to determine if I would suffer from "double NAT" issues?