Three common ways to inject an unwanted search engine are:

• add-ons (specifically, extensions)
• startup script file
• external malware

Let's start start with extensions:

Open the Add-ons page. Either:

• Command+Shift+a (Windows: Ctrl+Shift+a)
• "3-bar" menu button (or Tools menu) > Add-ons
• type or paste about:addons in the address bar and press Enter/Return

In the left column of the Add-ons page, click Extensions. On the right side, find the "Manage Your Extensions" heading.

If there is at least one extension before the next heading -- "Recommended Extensions" -- please continue:

Then cast a critical eye over the list below that heading. Any extensions Firefox installs for built-in features are hidden from this page, so everything listed here is your choice (and your responsibility) to manage. Anything that mentions search, or privacy, or looks suspicious, or that you just do not remember installing or why? If in doubt, disable (or remove). For your privacy and security, don't let mystery programs linger here.

Any improvement?

If your Add-ons page is blank or is blocked, you can restart Firefox in its Safe/Troubleshoot Mode to do the above review:

In its Safe/Troubleshoot Mode, Firefox temporarily deactivates extensions, hardware acceleration, and some other advanced features to bypass issues that can cause problems with pages.

If Firefox is running:

You can restart Firefox in Safe/Troubleshoot Mode using either:

• "3-bar" menu button > Help > Troubleshoot Mode... (before Fx88: Restart with Add-ons Disabled)
• (menu bar) Help menu > Troubleshoot Mode... (before Fx88: Restart with Add-ons Disabled)

and OK the restart. A small dialog should appear. Click the Open button (before Fx88: "Start in Safe Mode" button).

If Firefox is not running:

Hold down the option/alt key when starting Firefox. (On Windows, hold down the Shift key instead of the option/alt key.) A small dialog should appear. Click the Open button (before Fx88: "Start in Safe Mode" button).

Note: Don't use the Refresh without first reviewing this article to understand what will be deleted: Refresh Firefox - reset add-ons and settings.

Can you regain control of your searches?

I'm on a Mac - and I do not have any extensions installed.

You may have ad/mal-ware. Further information can be found in this article; https://support.mozilla.org/en-US/kb/troubleshoot-firefox-issues-caused-malware?cache=no

Run most or all of the listed free to use malware scanners. Each works differently. If one program misses something, another may pick it up.

NO Malware was found on the system.

"Browser Default" is definitely something I've seen coming from third-party apps or adware. Using the free version of MalwareBytes normally picks this up.

If not, then try looking for at you've installed around the time this started - some of these applications install extra things alongside and it isn't immediately obvious that is what they are doing if you don't read everything in detail.

The extension may not show up in normal mode, so try to start Firefox in Troubleshoot Mode.

Start Firefox in Troubleshoot Mode to check if one of the extensions ("3-bar" menu button or Tools -> Add-ons -> Extensions) or if hardware acceleration or userChrome.css is causing the problem.

• switch to the DEFAULT theme: "3-bar" menu button or Tools -> Add-ons -> Themes
• do NOT click the "Refresh Firefox" button on the Troubleshoot Mode start window

• https://support.mozilla.org/en-US/kb/diagnose-firefox-issues-using-troubleshoot-mode
• https://support.mozilla.org/en-US/kb/troubleshoot-extensions-themes-to-fix-problems