If you know the relative Url of the folder within SharePoint there is a straight forward way to access the files within that folder.

using Microsoft.SharePoint.Client;
...
using (ClientContext clientContext = new ClientContext("https://something.sharepoint.com/sites/mysite/"))
{
    Folder folder = clientContext.Web.GetFolderByServerRelativeUrl("/sites/mysite/root_folder/sub_folder");

    // Load the Folder and Files into the ClientContext so we can access them
    clientContext.Load(folder);
    clientContext.Load(folder.Files);
    clientContext.ExecuteQuery();

    foreach (var item in folder.Files)
    {
        // Load each file into the ClientContext to access the file information
        context.Load(item);
        context.ExecuteQuery();
    }
}