Well it’s kind of difficult to help without the specific error message. My preliminary guess is that your school has blocked connections to Proton VPN’s servers, in which case you are SOL.
If you’re a paying customer for Proton VPN, then this seems like something you should contact them about, since it’s their software, they should have a better idea of why you get this error.
Still doesn’t work for me it seems that it just times out after trying for 20 seconds.
edit: Since it seems to work on other peoples manjaro and its working on my machine with windows installed i think it might be some kind of network blocker.
I cannot guess what your issue is - I know one thing though - there is nothing with a default Manjaro installation which implements any kind of blocking or filtering.
Setting up firewall and filters for allowing or blocking traffic is not a responsibility of Manjaro - though some has an opinion that a firewall should be enabled - but for what I know it is the end user which need to implement such measures.
$ protonvpn-cli connect dk#14
Setting up Proton VPN.
Connecting to Proton VPN on DK#14 with UDP.
Successfully connected to Proton VPN.
Have you been experimenting with portmaster or opensnitch?