As for resume, it is awkward that there is a completely different word with the same spelling, but the sense is almost always clear in context; I do think that adding the accent marks looks a little fussy. There are, however, less common words from French and Spanish that turn up and probably ought to have accent marks.
So here’s the ruling. Go to whatever dictionary is the basis for your house style. If it shows words adopted from foreign languages with accent marks, use them.
Unless you decide not to.
In my view, the only reason to include accent marks in words that English has appropriated from another language (as opposed to proper names) is to cut down the potential for confusion. It should be clear from the context which meaning of resume is meant, continue or a brief written account of personal, educational, and professional qualifications and experience.