Here’s a completely just made-up theory that may bear little to no relation to the truth. English was invented in England, so they would be more likely to refer to someone by their city or region rather than the conglomeration as a whole. Similarly, France as an entity was constantly shifting and in very regular contact with Britain when English began to solidify in the Early Modern period, so they would be more likely to be referred to as Normans or Burgundians than ‘Frenchmen’ as a whole unit. Discuss and critique as you will.
Other nations for which there isn’t a non-gendered noun for an individual: Bangladesh, Burma, China, Japan, Lebanon, Netherlands, New Zealand, Portugal, Switzerland. This will likely become an issue of dialect.
What noun do you use to refer to someone form New Zealand other than the neuter “New Zealander”?
I can’t think of any noun for someone from Switzerland other noun phrases. I’ve never seen Swissman but only Swiss man. In any case, surely Switzerlander would be understood. And while those from the Netherlands are commonly called Dutchman or woman, a “Netherlander” seems fine.
Bangladesh - Bangladeshi
Burma - Burman
China - ?
Japan - ?
Lebanon - I usually use their ethnicity i.e. Druze, Marionite, etc.
Netherlands - Netherlander
New Zealand - New Zealander
Portugal - ?
Switzerland - A Swiss or a Switzerlander
Seems to me, and this is taken from my left elbow, as if words such as Englishman are simply the union of the longer adjective+(wo)man forms which exist for other peoples. Whether the majority of peoples get the adjective+(wo)man version, the adjective(wo)man version, or a word which is both noun and adjective requires more time spent counting than I can be bothered to spend. It does seem to me as if those where there are a noun and adjective which are different and which did not originate as slurs are the definite minority.
I think the idea is that for those countries, there isn’t a singular noun at all, gendered or non-gendered. You’ve never heard of “Japanman” or “Portugalman” , but we also don’t (usually) refer to an individual simply as a “Japanese” or a “Portuguese” using the adjective form as a noun, as happens with “Italian” or “German”.