Résumé, resume, and resumé are all accepted spellings in American English. As noted by others, many countries use the term C.V., which is likely to be a larger source of confusion for people.
Part of this is likely that many Americans do not have an easy way to type the accented 'e' character. (Short of copy/paste, I'm not even sure how I'd do it. Friends who have Macs have it easy.)
