There is a great number of languages using diacritics web.library.yale.edu/cataloging/music/diacrit
For example a simple phrase in French: l’été arrive à la fin. If one does not use the diacritics (or the correct diacritics) nothing will be found.
Or in polytonic Greek: ὃν οἱ θεοὶ φιλοῦσιν ἀποθνῄσκει νέος

Some software already does that, dtSearch (desktop search tool).

It could be added as an extra toggle button like the “W” (for whole word search).