Kindly, may I ask you to look up for and re-check your DNS records at Cloudflare dashboard for your domain to make sure the existing ones are:
A www
A mysite.com
Both with the values containing the correct IP address and also both being cloud (proxied via Cloudflare)?
Or you are using a CNAME type of DNS records?
Maybe you did not added the www record to DNS tab of Cloudflare dashboard?
Which would mean that requests are going to the host/origin server which is using and served over www (web aplication or some other content), but not having an proper SSL certificate (HTTPS)?
Or, you have got some redirection from www to non-www or vice versa, and possible having the issue?
Has the domain recently being added to your Cloudflare account? Maybe the Universal SSL hasn’t been issued yet, if so.
Here are the instructions how to correctly setup an SSL using Cloudflare: