@nicolas.maheu
First welcome to the Local by Flywheel Community. I’m real sorry about the issue with app going into active mode.
A common issue on Windows with other Local users is that BitDefender or a similar anti-virus will block the network access. Here is a previous thread on this issue [Windows] Why am I seeing ERR_NAME_NOT_RESOLVED when trying to access a Local site?
Do you have a firewall or anti-virus software running on Mac too? If its possible could you post the screenshots you are seeing from the browser?