Hi Tanguy,
First off, the reason the ‘+ Add Versions’ is grayed out is because it has already been used. This is why the darker engine tab is available, the one that says 4.3.1 in your screenshot.
Next, try the troubleshooting steps in the ‘Launcher is Unable to Download Content’ section in the link below. If nothing works, follow the 10 steps at the bottom of the page and post your ‘Verbose Logs’.