You would be naïve to think that, especially were you to write that on your résumé. That English has no diacritics is a façade built up to escape the fact that our keyboards make no provision for them.
(A little bit forced, but those are all English words I learned as properly having those appropriate diacritics, when I first learned those words back in grade school.)
Look those words up in the dictionary and they won’t have the diacritics, except as an alternative spelling. They’re loan words, and it’s a stylistic choice.
Ask 95% of laymen to write those words and there will be no diacritics, and the language is defined by its users.
The first entry is for "resume", the verb, which is a different word than "résumé", the noun. Note that none of the definitions provided for the verb "resume" would come close to working where someone intends to use "résumé", the noun.
Tell it to the New Yorker, where orthography like coöperate is required by official policy.
As they would no doubt also be happy to explain, the diacritic there is not correctly referred to as an umlaut, as "umlaut" refers to the difference in pronunciation between e.g. German "u" and German "ü", while the diacritic in coöperate doesn't change the pronunciation of any letter but instead exists to indicate to the reader that the two letter Os are to be pronounced separately rather than interpreted as a digraph (as in "troop").
It is somewhat interesting to note that modern English speakers often feel that a mark for this purpose is needed, even though formally the orthography doesn't call for it - but they are much more likely to write "re-emerge" than to write "reëmerge".
It's not difficult to find diacritics in use outside the New Yorker, though generally not in that use. One exception would be the common spelling "naïve".
(A little bit forced, but those are all English words I learned as properly having those appropriate diacritics, when I first learned those words back in grade school.)