That doesn't mean spelling them with the diacritics makes them not English.

French was the official language of England for quite some time so English and French have a special relationship, and any of the French diacritics are acceptable in English. English also has native use of the umlaut mark for as diaeresis e.g. coördinate.

For non-French diacritics, it is on a case-by-case basis. Most English speakers would accept ñ and even write it e.g "El Niño event". Nordic ø is questionable but would be accepted in place names. Phở is right out.

> Most English speakers would accept ñ and even write it e.g "El Niño event"

FWIW this may be true in the USA but in the UK and other non-NA English-speaking countries I don't think this holds.

You will definitely see jalapeños and such on UK food packaging. I just searched the bbc website for "jalapeño" and found this page [0] which uses both spellings (!). It also links to a page on "habañero" (sic) so yeah you can say that British familiarity with Ñ is somewhat of a mixed bag.

[0] https://www.bbc.co.uk/food/jalapeno_chilli