The index.html file will not interfere with the index.php file . Most browsers will give the HTML file priority, and load that first, but your problem has occurred as a result of the move UP the directory tree.
I trust you have a full backup...
If so, it may be a good idea to try the process again.
I do my moves (and I do a LOT of them) using CPanel. Now I don't know if you have the "proper CPanel" facility on your host, but if you do, then it's "safer" to make a COPY of the site that is in the subfolder, then MOVE that copy into the ROOT directory.
(I create a new subfolder called transfer and in one simple COPY/PASTE operation, I make a copy of the zencart subfolder into that transfer folder. Then, I move everything in that folder up to the root).
This process means that your EXISTING site is still safely tucked away in the sub-folder.
After you have moved the copy into the root, the only files that need changing are the configure.php files, where you simply remove the subfolder name from the path (where these are evident)
Unless you are intending to point at a NEW database, the DEFINES in the configure.php files relating to the database should remain unchanged.
You will need to adjust the CACHE reference, and this can be done either by running the fix_cache_key.php file (available in the Free Addons), or under the NEW setup admin console. My Store >>> Sessions .
Your new set up should work...
(I have managed to get this "moving" process done in under 5 minutes sometimes, so if a complete idiot like me can do it, then it should be within the realm of everyone else)