From index.html in the root directory, to the "consumers" directory where the blog is installed (shown without full syntax):
php require('consumers/wp-blog-header.php')
you cant use php inside a file named index.html
that wont work. .html files are static and php inside of them will not be parsed server-side.
If you rename your index.html to index.php, and try what I suggested you will see that it works as I provided (assuming you use the right path to wp-blog-header.php).
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I really should say that you CAN actually use php inside .html files, BUT that it requires an .htaccess tweek - which I am sure you probably have not made.