If you go to settings/search scroll down to search suggestions, you can deselect "provide search suggestions" If that is done IDK

Do you have a Google shortcut on the Firefox Home page (about:newtab|about:home) ?

The location bar drop-down list can show history items, bookmarked pages, pages opened in tabs, top sites, and search suggestions. You can set what suggestions show when you enter an URL in the location/address bar bar.

• Settings -> Privacy & Security
  Address Bar: When using the location bar, suggest:
  Browsing history
  Bookmarks
  Open tabs
  Shortcuts
  Search engines

• https://support.mozilla.org/en-US/kb/address-bar-autocomplete-firefox
• https://support.mozilla.org/en-US/kb/remove-websites-address-bar-suggestions
• https://support.mozilla.org/en-US/kb/firefox-suggest

Thanks Chris. I had already removed all other search engines, so nothing else even listed.

Thanks cor-el, I don't have a google shortcut.

I then unchecked all the firefox suggestions it did improve but not completely. If I now type googl it remains on my default search engine ... but the moment I complete typing google it reverts back to insisting on offering searching with google! Argh! It does say below "this time search with" offering me my default engine. I guess I have to be careful but the fact that google shows up at a is still a concern. I may have to clear history and cookies but really didn't want to have to do that. Thanks

not solved as of yet.

You need at least have a default search engine and have this selected on the "Settings -> Search" page and you can't remove/disable this default search engine.

• https://support.mozilla.org/en-US/kb/change-your-default-search-settings-firefox

You can disable searching via the location bar by setting keyword.enabled to false<\b> on the <b>about:config page.

• https://support.mozilla.org/en-US/kb/about-config-editor-firefox

That's a domain autofill since you have visited Google sites in the past, it has nothing to do with your default search engine. You can disable autofill in the address bar by going to about:config and changing browser.urlbar.autoFill to false.