If you've installed Wordpress then you've installed what is basically a stand-alone website, so your index or 'home' page is now Wordpress.
As I imagine it's php rather than html then you probably haven't over-written the old one and all your old site content should still be on the server, just not accessible because you no longer access the html homepage by your domain.
How do you upload your data? If using a conventional FTP program you should be able to see the files.
If you asked me what happens if you have an index.php and an index.html page I wouldn't know - but it looks like you've answered it yourself, the domain defaults to the index.php page.
I'm not sure what the best workaround would be. I'd imagine there's some kind of re-direct thingy you could do. "301" sounds familiar but no idea how to do one.
Alternatively delete Wordpress and reinstall on a subdomain, transfer everything to it and then copy over to the main directory - but that depends on how Wordpress works. You may then have to manually change lots of links, though hopefully it uses "/" rather than your domain with internal links.
For example a page called 'page1' should, hopefully, be '/page1.php'
Because then you'd have to change em all again. Might be no great trouble but if it's using links internally in the script it could be a nightmare to move it. So try a Google or something on 'moving a Wordpress site', see what's involved?
You'll also need, if going this route, a hosting provider that allows subdomains. Some do, some don't, some charge a small fee.
Another alternative is to creat a new directory, which is basically the same thing but looks more like
but that has the problem of being spiderable by search engines and can screw up your SERPS a little when changing over, but no biggie if you're just doing it while uploading content in the short term.
But primarily, the problem is Wordpress is a website, not a blog within your site unless you carefully set it up like that.