It's beyond easy to pair AirPods with a non-Apple device. And on Arch, it's trivial to have the AirPods appear in the bluetooth manager (in this case, blueman-applet)--but when you try to initiate pairing, it does not succeed.
The trick here--if you don't require pairing with Bluetooth LE devices--is to manually specify that the bluetooth controller (bluez) use BR/EDR transport rather than allow both transport modes.
Open a shell and do the following:
$ sudo vi /etc/bluetooth/main.conf
Uncomment and manually set
ControllerMode to BR/EDR:
# Restricts all controllers to the specified transport. Default value # is "dual", i.e. both BR/EDR and LE enabled (when supported by the HW). # Possible values: "dual", "bredr", "le" ControllerMode = bredr
Restart the bluetooth service:
$ sudo systemctl restart bluetooth