Makes no odds. Once you have the PAC code you can use it whenever you wish, even if the contract is still running.
What will happen is Orange will open your contract as per any other new customer. They will create this with a temporary mobile number and then add your PAC code to the order details. You will then be issued with your new SIM card - which will be linked to the temporary number - which you can begin using straight away. The PAC will then be processed and when complete, your SIM will take on your 'old' number.
Generally this is done way in advance of ending your contract, or is done as a way of ending your contract. But it doesn't cause problems that the two have been done separately
The only thing I would say, is the sooner you order, the sooner you get your new phone