Walking?
Unsolicited advice, so feel free to ignore it.
But if so, you may want to stick with the Frances, but once you get to Burgos, you can take the
Via de Bayona in reverse to Irun/Hendaye/or Bayonne - and direct train to Paris from there. You can also catch the Vasco leg of the same route in Santo Domingo de la Calzada. Either is a stellar walk, and more direct way to Bayonne than the Frances. Another alternative is to walk to Pamplona on the Frances, then to Bayonne on the Baztanes. It's also a bit more direct, but not as interesting as the VdB/Vasco. No Roman tunnels through the mountains....