Is the vCenter running as a VM in your Fusion or inside the ESXi?
You mentioned that you can connect to ESXi with vSphere Client perfectly.
Did you connect from your host (VMware Fusion)?
Are you using vCenter Server Appliance or Windows Based vCenter?
If a windows based, install vSphere Client in the vCenter, RDP into the vCenter, and try to connect with vSphere Client from the vCenter Server and see if it works.
Also note that when you are powering on/connecting a network adapter of the ESXi running on Fusion, it will ask you to input your username and password like below screenshot.
Make sure you input correct username & password, do not skip/cancel it.
