The highest point on the entire
Camino Frances route is at Cruz de Ferro (the iron Cross on the telephone pole where folks leave stones). This has an altitude above sea level of 1,505 meters (@ 4,950 feet ASL).
However, for many pilgrims, the first day out of St. Jean Pied de Port is the most challenging, even though this summit is not the highest you will encounter along this route. I suspect it is precisely because it is on the very first day you start out. Cruz de Ferro is a good three-to-four weeks later in your Camino. Also, the ascent is less severe than the first 3-4 hours out of St. Jean PdP.
As others have said, it is less an issue than commercial flying. The only issue is that you have to walk with your rucksack on your back to arrive there. THAT might cause intense breathing.
If you have any respiratory condition, or are not fully trained, just take it slow and be prepared. Stop as often as you feel the need. This is NOT a race. It is not an Olympic event.
As a "stocky" mid-60s guy, I find myself hacking up my lungs at the Napoleon Pass in the beginning, and at the other few challenging inclines. When I stop to catch my breath and others ask me if I am okay, I just tell them I am waiting for my two companions "Tweedle Dee and Tweedle Dum" to catch up to me.
That is what I playfully call my lungs... I explain that they are two squishy red bags with tiny legs slowly making their way up the hill behind me... The native English speakers find it amusing. The others are perplexed. In any event, once "the boys" catch-up, we are on our way once again...
I hope this helps.