English still sometimes (albeit very rarely) uses one type of diacritic. The diaeresis is in occasional use. Now days it is mainly used in the word "naïve," but it will be familiar to readers of the New Yorker on words like "coöperate."
The diaeresis is used disambiguate when a pair of vowels make two separate vowel-sounds, instead of one. For instance, if you didn't know better, you would think that the words "naive" and "nave" (said "nāv", the congregational of a traditional church) were homophones. But the diaeresis shows you that the "a" and "i" are said independently (nah-ēv).
Of course, English also uses diacritics occasionally in some borrowed words: résumé, née, fiancée/fiancé. But these are also considered optional.
The diaeresis is used disambiguate when a pair of vowels make two separate vowel-sounds, instead of one. For instance, if you didn't know better, you would think that the words "naive" and "nave" (said "nāv", the congregational of a traditional church) were homophones. But the diaeresis shows you that the "a" and "i" are said independently (nah-ēv).
Of course, English also uses diacritics occasionally in some borrowed words: résumé, née, fiancée/fiancé. But these are also considered optional.