If you directly connect Biarritz to Monaco you do get a pentagon and a reasonably good fit to the actual border; but the angle between the border and the coast

If you directly connect Biarritz to Monaco you do get a pentagon and a reasonably good fit to the actual border; but the angle between the border and the coast at Perpignan is so tight (well under 90° at higher zoom levels but close to a right angle even at a glance) that it feels like it ought to be a point of the surrounding polygon. (Treating the Pyrenees as a separate "side" from the Med coast also means that each side is either land or sea, not both.)