@lhari84 Thanks for your answer.
Yes I did reboot, multiple times. I actually tried several things. I even tried different available firmwares for the N30 gamepad, even older ones, but no luck...
...Until I tried to pair the gamepad "the hard way", i.e. manually, in the Linux console during an SSH session.
Then it worked. For those interested, the process is described here : https://github.com/recalbox/recalbox-os/wiki/Connect-bluetooth-controller-manually-(EN)
simple-agent did not work (method 1), but bluetoothctl did (method 2).
I have no idea why it refuses to pair in the GUI. I tried so many times, and it never worked.