Most search engines will determine the language based off of either the browser/OS language information or your estimated location. The language of your searches (in most cases) will not change depending on the language of your search term.

That would be extremely difficult since it would require some form of language detection system in the backend, which could be difficult since many words are shared with other languages.

Generally, you will either need to use the advanced search options for the search engine that you are using or go to a region-specific version of the search engine that you are using in order to change the language of your search results.

Hmm, I don't know. If I search for c'est la vie I don't think Google should assume I speak French. It's an interesting problem.

Since the results page language is largely determined by the search site, you might submit the question to them.

In todays world of globalisation and frequent trave to different countries, it is not practical to change the language setting on the options page of your browser everytime you do a search in another language than english. This is a problem Google should wrap their heads around.

Maybe so. Regardless, this isn't something that Firefox or Mozilla has control over. This is a feature that Google would have to create, so you're best option would be to bring it to their attention.

You never know. Maybe it's something that they would add.