Yes it's possible to use Proxmox. Do read the following topic:
http://forum.ovh.co.uk/showthread.php?t=1930
You have to make sure the server that you're using supports VT (Intel) or SVM (AMD). This topic describes a few things regarding that (and OVH has recently made changes to their website to better reflect which servers support this feature).
Given that, Windows can be quite demanding on resources to begin with, especially when you're talking about a game server. So an EG-series would certainly not be a bad choice.
You can use Proxmox for the Linux servers as well, no need to have both VMWare and Proxmox at the same time, as it kind of defeats the purpose - not to mention impossible. Have a little read in this topic:
http://forum.ovh.co.uk/showthread.php?t=2082
As for the servers being in France, you are correct. However, each dedicated server comes with a number of what is called a "Fail-over" IP addresses. These IP addresses are geographic, meaning that you can request UK IPs (or other countries that OVH services, provided you can give them a reason why you would need those). Such an IP can be assigned to your server - or in Proxmox's case, to each virtual server if you so wish.
You mentioned you're already running a VPS - it is possible to migrate VMWare, QEMU and OpenVZ images to Proxmox (which is based on both QEMU/OpenVZ). Have a look at
http://pve.proxmox.com/wiki/Migratio..._to_Proxmox_VE for more details. You may be in luck, and would simply need an sftp of the image, adjust a few settings and get back to business!