I flew from Canada (not Seattle), but same continent! I flew Calgary-Montreal-Paris. Then I took the train from Paris to Bayonne, and transferred to another train for SJPDP (same train booking through
oui sncf). I'm not sure if you have a specific reason for flying to Biarrtiz, but I really enjoyed the train from Paris to Bayonne. I landed in Paris midday Paris time and made my way via regular buses (the airports have buses to downtown) to a hostel that was walk-able to the train station. It was easy to find the 'bus to downtown' at the airport. I enjoyed the afternoon in Paris, and then slept at the hostel. I woke up and walked to the train station for an early morning train the next day. I got to SJPDP that afternoon, where I had time to explore and go to the office. I liked this breakup because it allowed some 'buffer' for delays, since the bookings (flights vs trains) are through different agencies (the train doesn't care if your flight was delayed, etc). It also allowed me to acclimate a little to the time difference (west coast NA to Europe is enough to mess you up!).
On the way home, I flew from Santiago to Paris, and then from Paris back to Montreal. I took a bus from Santiago to the airport (again, very easy to find...literally anyone can help you find it). I had a very long layover in Paris (again, intentional so if the Santiago flight had issues, I had buffer). I had originally planned to sleep in the airport in Paris. However, I felt I had spent less than expected on the walk, and found through (I think just google? maybe hotwire?) that there was an airport hotel across the street from my terminal that wasn't too expensive, as they had those tiny rooms that are clearly designed for 'sleeping only'.
That was probably a longer story than you wanted, but there you have it! It was long on both sides, but compared to 6 weeks of walking, it wasn't too long! I liked having the low-stress, spaced out itinerary. Also, trains are SO COOL. I love the high speed rail in Europe =)
P.S. I booked my flights through 'kiwi', which is a 3rd party booking agency that 'combines' itineraries from different airlines. I do not recommend this. I had no issue with it, and it was cheap and it all worked out well...but I still don't
recommend it. One of the airlines I flew on since went out of business I'm pretty sure. I booked the flights ~6 weeks before departure. I was only comfortable with this because I wasn't going to be heartbroken if it all went belly-up (I made my peace with that). That's why I don't recommend it - this type of flying can totally ruin your trip if someone goes out of business, or there's 'incidents' that aren't covered by the 'terms and conditions'. HOWEVER. You should be able to find overseas flights through a hopefully-stable-ish airline, and then do your own separate booking for the Santiago connector flight as long as you give yourself a day's buffer. Just my (way more than) 2 cents for ya!!
BUEN CAMINO!
(I'm taking the train to Seattle tomorrow morning for a bike adventure! Haven't been in years. Very excited!)