The annual "high season" runs from Easter to about mid-September. During this time most folks tend to use their vacation or holiday time.
Also, there are many national holidays across Europe, and some in other countries too from Easter through early September. People use these holidays as a starting point to conserve their personal holiday time to do Camino. "Bridge days" are frequently in play here. As a result, there are spikes in Camino traffic around these national holiday weeks.
Also, once universities and most all schools let out for the summer months, by mid-June, things really heat up, literally and figuratively.
The "high season" continues until the schools and universities are back in session by mid-September. Most folks have finished their annual vacations / holidays by then as well.
As always, the "trick" is to figure out where the pulses or peak surges will occur and then plan your departure around those dates. You want to be a day or two behind, or ahead of these surges.
From Saint Jean Pied de Port, if you could further parse the September numbers from the Pilgrim Office, I believe you will find a very large "pulse" or peak surge, departing within the first two-weeks of the month. The seasonal drop-off occurs around mid-month. The monthly total remains very high, but the distribution within that month is skewed towards the early part of the month.
I am thinking about doing my 2018 Camino from Saint Jean PdP as my sixth Camino. My thought is to depart around or just after 15 September, and to reach Santiago towards the end of October.