Pi-hole arrete de fonctionner avec ma livebox 5 de chez orange

Thats not a true static IP but a static DHCP reservation instead.
The D in DHCP for dynamic.
What do you think happens with that DHCP reservation when you disable the DHCP service on the router to let Pi-hole take over?

If the Pi is to function as a DHCP server, it needs a true static IP configured manually on the Pi itself.
A DHCP server cant assign a DHCP lease to its own interface.

Check if below one is enabled:

systemctl is-enabled NetworkManager.service

If enabled, you can configure "manual" static details on the Pi with below (Network Manager Text User Interface):

sudo nmtui

Example config below (dont mind the lo profile for the loopback interface named lo):