how to get from Logrono back to Bordeaux?

Bus to Pamplona, maybe? They have an airport and flights to Paris I think.

Try bus to Bilbao, flight to Orly/Paris on Iberia or Vueling or flight to CdG/Paris on Air France.

MM

We went from San Sebastian by train to Bordeaux very easily. I would think that Bilbao would work the same as it is just a bit earlier on the route.
The train goes from S. Sab to Irun/(French border joining Irun forgot name) and then onto a French train. The same train goes onto Paris so there would be no need to stop in Bordeaux...unless you wanted to.
Bordeaux is really worth a stop. We visited some Camino friends there and were taken back at what a great city it was.

The best option is probably Renfe. Renfe operates trains from Logrono to Miranda de Ebro. Then wait for a train from Miranda de Ebro to Irun/Hendaye. For some reason Renfe site will not connect the dots on a query for Logrono to Irun.

Renfe
http://www.renfe.com/EN/viajeros/index.html

Estellesa has a bus (or two depending on the day) from Logrono bus station to Irun Renfe Station.

The Estellesa itenerary states it also has a stop at Irun-Front Hendaya. If you can confirm that is the SNCF Gare d'Hendaye - that is the place you want to go. Otherwise get off at Irun Renfe Station.

Estellesa
http://www.laestellesa.com/

Autobuses La Union operate from Logrono to Bilbao Termibus
From Termibus walk to San Mames Station and take Euskotren (every half hour) from San Mames to Hendaia.

Autobuses La Union
http://www.autobuseslaunion.com/PDF/Bilbao-Logro%F1o.pdf

Euskotren
http://www.euskotren.es/

If your Renfe train or bus ends up at Irun and your SNCF train leaves from Hendaye ... take the Euskotren from Irun Colon Station to Hendaia Station. Exit Irun Renfe Station, turn right, cross bridge over tracks to find Euskotren Colon Station on left (north). Hendaia is co-located with Gare d'Hendaye.

SNCF TGV and Intercites trains leave for Paris from Irun and make a stop in Hendaye.

Depending on your timings, you may need to catch a TER train. TER trains leave from Hendaye towards Bordeaux where you transfer to TGV to Paris.