You could combine everything into one WP installation. It wouldn’t be too hard to have all the posts prepended with the blog directory, so their URLs would stay the same. You would basically do a bit of permalink setup and import the content from the blog site into the new site.
Or, you could run two separate WP installations. The user would have two separate sites with potentially two separate logins, which is often less than ideal, but you’d set up the new site on their hosting and just keep the blog folder intact. Anything inside the blog folder would be the original site and anything outside it would be the new site.