OpenVPN, internet access and settings of the "wired connection"

“not maintained by Freedombox” suggests that the interface might have an entry in /etc/network/interfaces that you need to comment out or delete. From this thread:

If you comment out your network/wifi cards in /etc/network/interfaces that allows NetworkManager to get full control of those interfaces. Freedombox uses NetworkManager to configure networking, so by doing this you are using the configuration method expected by the Freedombox team.

But since that issue is on the first box where you already can access the Internet over OpenVPN, I don’t know if it helps explain why the two boxes behave differently.