In Windows 10, many of the in-browser options for setting them as your default browser don't work, and I suspect that's what's occurred here. If you wish to set your default browser it is better to do so via Settings, Apps & Features, Default apps pane, Web browser item. That item should give you a dropdown list that includes all web browsers that are installed on your system and allow you to choose whichever you'd like to have come up when a link needs to be passed to a browser, such as from an e-mail message.
After setting your default browser to Firefox, get into Firefox and open the main menu, choose the Options item, then choose the Search pane in the dialog that comes up. Default Search Engine is included there and you'll get a dropdown that allows you to choose it. I have yet to see Google not listed in the list of search engine options that come standard with Firefox.
Brian - Windows 10 Home, 64-Bit, Version 1709, Build 16299 (dot level on request - it changes too often to keep in signature)
The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.
~ Niels Bohr