First of all, does he REALLY need 64-bit Office? The chance are that he doesn't and would be better off with just 32-bit Office. Microsoft currently recommends against installing 64-bit Office and your user must have went out of his way to get it to install 64-bit.
But assuming there is a legit reason to use 64-bit Office (most having to do with Excel, and next to none for any other programs, actually) then you'll have to update your application to work with 64-bit Access. There are 3 general considerations:
1) If you have linked tables to big databases such as SQL Server, Oracle or whatever, you need to be sure there's 64-bit driver installed on the computer. With SQL Server, it should be already installed (comes with Windows) but this may not the case with other RDBMS if you're use any of those.
2) If you're using any ActiveX controls, you'll have to either disable, remove or update to a control that is 64-bit. This is more serious because there are not always 64-bit replacement. A good example is if you have a TreeView control from MSCOMCTL.OCX. There are no 64-bit MSCOMCTL.OCX so you have no replacement for that and thus your TreeView would not work. You'd probably have to look at third-party ActiveX that is 64-bit compatible if you really wanted to keep TreeView in 64-bit Access.
3) If you have any API functions in your applications, then you have to update the statement. Grover Park George has a blog post about this process
here. Hopefully it'll give you an idea of how you can update your declarations.
If your application doesn't have any ODBC linked tables, ActiveX controls and API functions, then it'll work as it is without any modification. It's obviously rare that such applications are not that complicated.
PS: Oh I forgot to mention -- you can't share a *DE file between both 32-bit and 64-bit OSes. You'll need to compile a new *DE file for 32-bit and 64-bit separately and distribute the right file to right people. That applies even if you didn't have any ODBC drivers, ActiveX controls or API functions at all.