I suspect that the answer is that, for historical reasons, there are a large number of people of South Asian origin in the UK and many fewer of any other sort of Asian origin.
4.9% of the population in the 2011 census described their ethnicity as "Asian or Asian British" and chose the subcategory Indian, Pakistani or Bangladeshi, and a further 1.4% chose "Other Asian" (there is a separate category for Chinese, 0.7%). Many South Asians identify as Other Asian and not with any particular South Asian country (particularly common among Muslims who, or whose ancestors, immigrated from what is now India), so it's fair to conclude that ~5% of the UK population is South Asian and only 1-2% are any other sort of Asian.
The US race question in the 2010 census is different from the UK ethnic-origin question, but the overall Asian-American population is 4.8%. I could not find a breakdown, but Chinese and Filipino-origin Asian-Americans are the most established and largest communities.
"Asian" has come to be used to refer to the prototypical Asian in both countries - which is a South-Asian origin in Britain and an East Asian origin in the US.
British people, incidentally, are much less likely to use "Oriental" to refer to East Asians than we were in the 1980s, because we've absorbed the sense that it's offensive from American media. We might use it if fishing for a term - "East Asian" is not a category that comes to mind because it's not one that Brits deal with much, and the overwhelming majority in the UK are Chinese (ethnically; many Chinese in the UK immigrated from Chinese-minority communities in former British colonies in South-East Asia).
Best Answer
Frenchman is not gender specific:
However, Frenchman does not = "French man" or "French woman."
"A French person" constitutes the gender neutral form of these.
Use the accepted "Frenchman." To address someone as a "French person" sounds awkward and contrived in my opinion.