This might be a silly question but why would their be two index files?
Several reasons. Might be files left over from a site that was created in another program that published using the .html extension.

Or you might have published using index.html for your save as name, and then published changes and just saved as the default index which exports as index.htm

In the olden days, PC computers could not support file extensions with more than 3 characters. On the other hand the Mac could use long extensions if they wanted to.

And for whatever reason (perhaps Mac bias) the full extension took precedence over the shortened version. All browsers accept both extensions.

The best bet is to delete all the files on the server and republish your site. Then you will only have one version of the site posted.