I have recently had some searches that give results not expected or wanted. Apparently at least on some occasions Google considers character with and without accent to be equal. In my experience it can be rather annoying. Unfortunately I can’t remember any of my original searches so I made one up. Let’s say you’re searching for “siil naha” (without quotes in search) then you also get results containing “näha” even though it is completely wrong because the meaning of those words are very different. I can understand that with “Émile” and “Emile” it helps but not with every word that has an accented character.
Edit: while I was typing it in I also realised what would be the solution. You can use “siil naha -näha”. Of course without quotes if you’re not searching that specific phrase (and why would you search for such meaningless phrase). Now that I think about it, it would be nice if Google displayed some kind of notice when it uses accent-insensitive search and a clue how to change it to accent-sensitive one. Perhaps some checkbox in advanced options?
Edit 2: after some more careful looking, results containing “näha” also contain “naha” either in text or in links to result page. However emphasizing both words in search results can be confusing. It certainly was for me.