Yahoo is trying to up its game and it is trivial to choose your default search engine.

But if something on your system keeps changing or overriding your settings, such the "Searchme 2.5" extension from Spigot which is listed in your More System Details and is recently afflicting many Mac users, then you need to remove that:

http://www.spigot.com/about/contact-us/uninstall-spigot-mac-extensions/

Also, the answer to your question is: Mozilla only has an agreement with Yahoo for North America.

Thanks. That was, indeed the issue. Spigot was also present in the German edition of FF V 38.0.1.

As well, I re-installed the North American version of FF and saw that someone had written a new add-on, "Default Search Engine 3.3", which does indeed allow one to permanently banish the yahoo search engine from FF. The earlier reviews of this add-on were very negative, but the newest version was just updated two days back, and performs as advertised.

Strangely, it was already installed, even though this is still FF V 38.0.1 . Some irony, there.

You don't need an extension to select a default search engine and have Firefox remember it. Mine has been the same since I switched it back in January. If yours changes, something is changing it. Feel free to follow up if it happens again.