That could also be due to a missing HTTP to HTTPS redirect for example. Or perhaps you need to associate the certificate with your site first for HTTPS to work, I dunno. See your hosting providers knowledge base for more info. I don't think switching to Let's Encrypt will fix anything related to such things, as it will only change the certificate authority which is issuing the certificate. It won't magically fix incorrect settings at the webservers part.
Also, currently your entire site is down. Not related to SSL. HTTP is down too.