What will happen if I don't pay a bill

So basically I was using a service that host web server and also allow me to register domain name in Europe.I moved that another country in Asia where I'm living now.Usually that website will send me a mail 60 days before renewing and doesn't do it without action from me.

They did send a mail 1 month before the renewal to explain that from now without action from new they will renew it automatically and unfortunately, I didn't notice this mail.

So 1 week ago they actually went ahead and sent me an invoice for a service that I'm not using and don't intent to use anymore. I directly sent a ticket to let them know what had happened but basically they just say that it's too bad for me.

The thing is on the invoice they use the address from my old country and I'm not even legally a resident in that country anymore.The other thing is I don't have a credit card here, so even if I wanted, I can't pay them right now.

If I just decide not to pay what will actually happen ? Am I in trouble ?

Edit for location: Right now, I'm living in Japan; before I was living in Belgium and the service is provided by a french company.