In this paper, we address the problem of coordinating platoons of connected and automated vehicles crossing a signal-free intersection. We present a decentralized, two-level optimal framework to coordinate the platoons with the objective to minimize travel delay and fuel consumption of every platoon crossing the intersection. At the upper-level, each platoon leader derives a proven optimal schedule to enter the intersection. At the low-level, the platoon leader derives their optimal control input (acceleration/deceleration) for the optimal schedule derived in the upper-level. We validate the effectiveness of the proposed framework in simulation and show significant improvements both in travel delay and fuel consumption compared to the baseline scenarios where platoons enter the intersection based on first-come-first-serve and longest queue first - maximum weight matching scheduling algorithms.