Dp - without wishing to split straws at PA28 speeds I think the north coast of France was more liek 45 minutes from the search area. Do I also think for some reason it was not long before darkness fell? If so, with no panel lights, the possibility of a ditching and maybe no night experience there were further influences at work.
SSE would probably bee the better option given the pilot should have had a good idea of how far south he was if less idea how far east or west. The peninsula would have been closer and difficult to miss.
As I said earlier if he didnt feel he could reach land for whatever reason and knew those waters reasonably well he would also know that there isnt much shipping or small boats around at this time of the year once you get outside the shipping lanes. There are also some nasty currents and overfalls even in light winds - you can tell I have been in the waters around there on the odd occasion (as well as over).
What was going through his mind and what problems he had we really dont know and certainly we have learned not too trust the Papers. I am therefore as always very reluctant to speculate but felt the point should be made that any pilot out of sight of land, short on fuel, not sure of their position, with darkness impending and a total power failure is being put to the task before we jump in create the impression that a safe outcome is predictable.