Welcome to Manjaro forum @RaphaelDeck
To disable headphone jack detection:
Find the audio card number for the onboard audio analog output from:
aplay -l
(most likely to be either card=0 or card=1)
Then install alsa-tools package
pamac install alsa-tools
Run jack-detection tool with headphones plugged in and unplugged
sudo hdajacksensetest --card=0
If responses show: (Green Headphone, Front side): present = No even when headphones are plugged-in, run the jack re-tasking tool:
sudo hdajackretask --card=0
Enable Advanced override and Override for the Green Headphone, Front side jack
Change Jack Detection to Not Present and click on Install boot override
Reboot system to load jack override