Since over 23% of top websites are using WordPress, I'll take a punt and assume your site is using WordPress...
Install Duplicator Plugin - It'll let you backup All of your site (Database included) and it'll allow you to relocate the site to another domain/host. Not that you'd want to leave x10
YouTube Video on how to use Duplicator - here
I best mention that if your site is huge with large pictures or files, then there's a good chance a Free Hosting service will time it out. Resources are limited for good reason.