Lots of choices:
You can install WordPress in the webroot and it should ignore existing files. (set up the permalinks however you'd like. the rewrites should ignore an existing file. Make sure this is the case for your server) where you can serve the existing .html files and WordPress side by site.
You can install in a subdirectory, ex. domain.com/blog. Then link as needed into the static site's navigation.
Or you can import the .html pages into WordPress, serving with the same .html extension for the .html *pages* via plugin, adding the blogging functionality. (this if they'd like to manage the whole site from one place. the blog related posts/categories/tags related pages won't necessarily have the .html extension unless you config that way.)
In the first two cases, theme WordPress to match-up with the main site, in the last, it's a theme for everything on the site. Lots of choices for you.