One of the best military axioms: "All the best plans have a tendency to go awry".
Even if there are no delays of any sort how long will it take you to just get off the plane?
Unless you are sitting in 1st/Business class Row 1 it could easily take 15-20 minutes.
Walk to the customs...I have no idea where they are at but I'll generously give you only 5 minutes
Get through the customs... depends on number of agents working and overall number of people...maybe a non-issue to you as an EU member... but say another 5 mins to get outside, another 5 to get to the taxi throw the backpack off and sit down
I actually show 16 minutes to get to Gare de Bayonne "in current traffic" which is no traffic at all let's say your luck still holds...
Do you know the layout of the Station?
Do you need some time to find out what track your train leaves from and then get there?
Another 10 minutes to be safe?
I think you just missed your train by a couple of seconds....
And all the stress and anxiety
! Again as
@trecile alluded What a way to start a Camino!!!
Here is a thought seems it is slightly over an hour to take a taxi straight to SJPdP from BIQ. I say if there are no issues you can bank on ETA of 1:30 pm
BTW are you planning on stopping at the Pilgrim's Office and if so is "the plan" that there will be absolutely nobody there ahead of you and you'll be in and out in matter of nano seconds?