A resume by any other name is still a resume. Even if it's the dreaded résumé or, worse, resumé. I'd rather you call it a curriculum vitae, even though 99.99% of curriculum vitaes are really just resumes. So, what's the correct way to spell it?
First, one quick point. The most likely place you will actually type the word "resume" is in your cover letter, as in "my resume is attached for your review" or something similar. If you use it more than that you're likely over-using it.
Ok, now that I've got that out of the way, it is time to ditch the accent. Just use "resume". It's cleaner, and given the context, the reader will never confuse it for the homonym, resume (the one pronounced ree-zoom).