Jodie, a dictionary will back you up on any variant except having a single accent on the first syllable. Pronunciation does not follow spelling; it follows your meaning.

Like, from my NOAD2:

résumé |?r?z??me?| |?r?zu?me?| (also resumé or resume)
noun
1 a curriculum vitae.
2 a summary : I gave him a quick résumé of events.
ORIGIN early 19th cent.: French, literally ‘resumed,’ past participle (used as a noun) of résumer.

CV.

But if you want to be French and use resumé, go ahead and include as many acute accents as it takes to make you happy and your word choice unambiguous.