Mozilla fixes the default Search Engine Restore Issue in Firefox 45. The latest Firefox 42 and earlier versions had a restore default search engine bug which has been fixed by Mozilla in Firefox 45 (Nightly).
The bug -‘ “restore default engines” button should also reset the selected engine to the default ‘ is when you remove the default Search Engine in Firefox and ‘restore default search engines‘ using the button provided in the Search preferences, the default engines were re-added, but the default search engine doesn’t get changed here, previously selected engine was still used as default for Searches in Firefox browser.
The company has fixed this in version 45. “It’s generally confusing to have this button (restore default Search engines) only re-add the default engines, and not also reset your selected engine to the default.”