In older texts the notation appears on other words like coöperation. Some Americans use dieresis in their names as well (Zoë and Chloë are increasingly common for example). Furthermore the dieresis (trema in French) in naïf is doing the same job as a dieresis in English, so it can be easy to make the claim that we got all dieresis from French, but in reality it seems to have been borrowed from Ancient Greek as late as the 1600s, and gone directly from Ancient Greek texts to the languages that use the notation today (Galician, English, French, Occitan, Dutch)