Full disclosure: I’ve never actually created a multi-language site.
That said, there are two common ways to go here. One is to create two virtual domains (or just two separate subdirectories under public_ftp), one for each site, in separate directories as described here:
http://svn.modxcms.com/docs/display/revolution/Creating+a+Subdomain+from+a+Folder+using+Virtual+Hosts. Each directory will have its own index.php and config files. Only one of the directories has a MODx install, which is shared by both contexts. In this method, if the two sites have different assets (images, files, etc.), they can have the same names but different locations. The index.php file initializes the appropriate context.
The way other is to have a single directory, but change the context with a plugin based on the URL that the user comes in on as described here:
http://svn.modxcms.com/docs/display/revolution/Using+One+Gateway+Plugin+to+Manage+Multiple+Domains. Different assets would then have to have different names (or at least a different prefix).
In both cases, you’d want to create context settings in each context for the various paths and URLs (e.g. base_path, site_url, etc.).
I hesitate to say which method would be better for you since I haven’t used either one for a live site.