My current plan shows that it has a 38.17/ month phone payment included on a 24 month contract.
I'd like to renew the contract and pay the difference between the full price of the phone and the 24 month charge (I.e. 1800 - 24x38.17) = 884
Fido recently change to a device financing structure only, since you just finished with your old contract it's most likely your plan is not compatible with the new structure and you would need to switch to a current in-market plan in order to finance a new device or you can keep your current plan but it will continue as a month-to-month plan and you will not be able to finance a device.
You can get more information regarding the new Fido Payment Program here.