Actually, all three are correct. From http://en.wiktionary.org/wiki/r%C3%A9sum%C3%A9#Usage_notes -- "In the US, there are three major spellings of this word: résumé, resumé, and resume. All three are in common usage and all three are occasionally contested. The usual justification for each is usually as follows..."

Update: Being pragmatic, I should probably use "resume", because that's how Google Jobs spells it.