Omnia 2020 for Iliad. Does the modem have a phone output? And if yes is a traditional connection or a VOIP?
No, the omnia had no analog phone port nor a SIP/VoIP base functionality. You will likely need to add a separate unit for any of that.
Personally, I faced that reality a decade ago, when switching to CeroWrt/OpenWrt (the ISP router really was a pain in the a** so I was willing to spend some money to be able to leave it behind…). I bought a relatively cheap gigaset SIP base with a dect phone (as far as I know there are no opensource dect basestations, but I have not searched all the hard) and that is now working decently for over a decade.
At least in Germany AVM FritzBox routers can be gotten 2nd hand for little money and can be “pressed into service” as pure Telephony base by configuring them for using one of the switchports as wan using DHCP and filling in the ISP’s SIP credentials, not sure how easy that would be for a french/illiad sip account, but my gutfeeling is that should not be impossible either.