How can I get VMWare Fusion 4.0 to work on Mountain Lion?
Upgrade to the latest version of VMWare Fusion, in your situation you will need manually download it as indicated below for the situation you describe in your question:

I upgraded to Mountain Lion and now VMware Fusion 4 won’t start. What happened?
Mountain Lion appears to detect some older versions of VMware Fusion 4 and prevent them from launching. To resolve this issue, login to http://my.vmware.com/ (free product registration required) and download VMware Fusion 4.1.3. It can be found under “Products &amp; Downloads &gt; All Downloads &gt; VMware Fusion”

According to VMware Fusion and OS X Mountain Lion FAQ