No, you don’t have to use your Frasers Plus account if you spend your Reward and have any further balance to pay. You can use any payment method to cover the balance.
E.g. if you have a £10 reward and the full purchase price is £29.98, you can use your £10 Reward and pay the remaining £19.98 using any other valid payment method, not just your Frasers Plus account.