I expect like you, I am a keen reader of the various biking magazines and this edition of RiDE got my attention due to the reference to Pyrenees.
More than that article, it had a great piece from their "staff" Lawyer, answering a question from a reader that had (unfortunately) had an off, and now needed to get his bike back home.
I can't re-publish the article here, but the gist of the reply was:-
If you do have your bike damaged and recovered to a garage, make sure that you get a depennage (if you are not too hurt of course...) which is the recovery dealer detail and paperwork, often handed to you by the Police at the scene.
The recovery will likely cost around €100-120 and storage will run to about €2.50 per day. All negotiations and paperwork will be in local language by the way.
Be careful of recovery dealers that take the bike to a shop that are not bike experts trying to get the repair work - the Lawyer mentions a new BMW bike being repaired by a Renault garage.....
If you bike is so damaged that you want to write it off in France, this seems to be impossible for a British registered bike - you can only do that with a French Carte Grise. So, it needs to come back to UK... Plus you will have British Insurance, which will require an inspection, so the bike needs to come home.
European Insurance or Breakdown will save you from much of the above - they all have French / Spanish / Italian speakers and will co-ordinate all this stuff.
Some of this may appear obvious and none of us wants to have a crash or damage when in Europe, but I personally cannot stress enough that you should both check your bike warranty AND get European Breakdown, which includes recovery.