You have updated Firefox to its latest version (v 41.0) and have since noticed that Windows 10 and Cortana searches no longer open with Bing. Instead they open with your browser's default search engine.
This problem occurs when you are using Firefox as default web browser on Windows 10 (you have recently updated or installed Firefox on your PC). Mozilla introduced, in the latest version of Firefox, a new feature allowing the web browser to edit the default search settings of Windows 10. Basically, if you are using Google as default search engine in Firefox, then the same settings will apply to Cortana and Windows Search. This feature is enabled by default, but you can turn it off in a couple of easy steps:
Open Firefox, click on the Menu button and then select Options. Go to the Search section > Default Search Engine and then clear the Use this search engine for searches from Windows checkbox: