You write just like everyone normally writes, by dropping the accent. I only see such spellings when people are trying to convey some sort of sophistication, rather than in casual, day-to-day use.
Precisely. Even when writing by hand, where there are no character encoding limitations, I've never seen anyone add the accents to "fiance" or "cafe" or "resume" when writing in English.
"I only see such spellings when people are trying to convey some sort of sophistication"
McCafe and Buckingham Palace would want the "sophistication angle". Both spellings work obviously, but IMO (and the majority of English books) "cafe" is the "correct" spelling.
Other languages figured out good compromises, e.g. Dostoyevsky is transliterated from Достоевский; the name of China's current dictator doesn't even render in my browser, but is transliterated to Jinping Xi. German passports have the German version for humans, and a standardized, transliterated version for computers. Gößmann becomes GOESSMANN. I see no reason why the same thing can't happen; just drop the accent from the E. Also, for some reason, my browser shows that E as having no accent, if you want an illustration of the problem.
A nitpick: Xi is his last name, but Chinese names are generally transliterated in the Chinese order of LAST FIRST ("Xi Jinping"). If you do a verbatim Google search for "Jinping Xi" you'll get around 500 results.
If a Chinese person adopts an English name, they'll put it first, however. Eg "Jake Ma".