1. A method for optimizing the monitoring of an optimal flight plan of an aircraft relative to a predetermined cost index, the predetermined cost index inducing optimal values of an arrival time and of a quantity of fuel remaining on board that are estimated to destination for the flight plan and the predetermined cost index, and further comprising a process of overriding the arrival time and quantity of fuel remaining estimated to destination on the optimal arrival time and quantity of fuel remaining values, the process comprising at least, at each flight phase of the flight plan, a step of computing the current estimated values to destination of the arrival time and quantity fuel remaining on detection of at least one external constraint modifying the flight plan, and their difference from the optimal values, and the overriding process supplying as an output a corrective cost index that is applicable on at least a portion of the remaining flight time, and a corresponding modified flight plan.