Did you follow along the step by step instruction as described here: Change your default search settings in Firefox

Yes, I tried that however when this happens, the ONLY default search engine in the dropdown is Amazon. The One-Click Search Engines also only shows Amazon and the "Restore Default Search Engine" button is disabled.

Did you install or use any Add-ons what might overwrite your default search settings? It sounds like corrupt Preferences. Try also to delete the Firefox preference files. Check out Refresh Firefox - reset add-ons and settings

No Add-ins. I just tried this again to make sure of the steps and I have more detail. English (US) was my default and only language. I added French. In French, I had all the search engine options. I went back to English (US) and then Amazon was the only choice. Refresh Firefox fixes the problem, of course, but then the languages are gone so that defeats the purpose.

Jake, I am able to reproduce your issue. Firefox looses the default search setting. I don't know if this a bug. Firefox sets different search settings for every language. If you need to switch back and forth a lot e.g. French and English, you could also the Firefox Profile feature Profile Manager - Create, remove, or switch Firefox profiles

If you think this is a bug I do recommend to fill a bug report. Simply send send your comment via email to ios-feedback@mozilla.com or go to Firefox > Settings > Send feedback

Thanks. Not sure it is a bug but it seems like it is so I submitted it via Feedback. I looked at the profiles option and while not seemless, it seems that a profile for testing websites is exactly what profiles where created. Marking your comment as solved problem.