We do, of course, use accents and other diacritics. It's not as common as in other languages, but most people will come across a few each day. The popular argument here is that many are French, with the accents optional, yet soupçon and exposé are rarely written naked. If you want non-French, pick up the New Yorker and you will find coöperative and reëlect, or a poem to find changèd and learnèd. We use them in names, from Brontë to Beyoncé.

There is an excellent Wikipedia article that goes into detail on the subject: https://en.wikipedia.org/wiki/English_terms_with_diacritical...