Our father (debirentier) predeceased the sellers (crédirentiers) of the property he bought as a life annuity. As the deceased's heir, do I have to continue paying the annuities until the sellers die?

Yes. As part of your father's estate, you inherited the property he had purchased as a life annuity, as well as the related debts. It is therefore your responsibility to continue paying the annuities until the death of the seller.