If I understand you right, the Mint menu search isn't searching the web using your term? I'm not familiar with Mint's search, but I would consider that undesirable behavior if it were so. That's a feature :^P
On the Firefox search box, use the dropdown menu to select a different search provider. I like DuckDuckGo. It looks like they don't give you Google by default, so you'll have to install it by clicking the "manage search engines" options in the dropdown box. If you insist on Google, I'd recommend StartPage as an alternative. It uses Google search without the tracking.
For searching from the address bar, see this page...
https://support.mozilla.org/sv/kb/search-web-address-bar
This is my search string...
https://duckduckgo.com/?q=!+
This searches DuckDuckGo using the I'm feeling Ducky protocol. IOW same as Google's I'm feeling lucky. You get a page, and hopefully it's good :^D