My partner is worried that Google will think that the site has been hacked, or no longer relevant. Is this true? Can we let Google know that we're changing our site?
It's extremely common for sites that migrate to a new setup and a lot of them will have URL changes such as
index.html to just
home.html - If your partner whats right then Google would be receiving complaints in the millions.
Thankfully its not true, there isn't anything within Google Webmaster Tools that you can say we have moved this page to that, but there is if you was moving from one domain to another, but since your not you can't and its a bit more complicated.
You will need to look up how to edit he .htaccess files and setup various redirects. What this means is that when old pages are accessed for whatever reason the user is then redirected to the newer page meaning there experience is not dampened by your upgrade.
Depending on how many URLS you may want some complex URL rewritting since if you have 1,000's of URLS then the htaccess can become large and the site can slow down as a result.
If you don't have 1,000's of urls or least not all of them need redirecting becuase you don't think people will notice then you can use the mod_rewrite using:
Redirect /old-path-name/ http://www.domain.com/the/new/path
There's 100'000's of guides on HTACCESS on the net and many on PRO Webmasters so I won't go into to much deep, you're need learn some basics.
So your first point of call should be redirecting
/ to home.html that way Google understands that the page has moved, and people don't get the old site.