I don't think there can be an answer any more objective than, "that's just how he felt." These terms today are acknowledged to be social concepts of personal identity, rather than something with any kind of scientific grounding.
However one suspects that his choice of Englishmen, Scotsmen, and North Germans is far too close to the ethnic makeup of his native Philadelphia for coincidence. If you find the inclusion of Germans (and nobody else on the continent) a bit odd today, note that 100k Germans had immigrated to Pennsylvania prior to independence. At the time this was written about ⅓ of the population of Philadelphia was German. So when he was describing "white people", it very much looks like he was just describing the vast majority of the population of his native Philadelphia in an inclusive way.
I know that today this looks rather ... limited ... on a world map. Note that in the USA the concept of "whiteness" has a history of expanding to include more and more immigrant groups (while some groups, like natives and Africans are always definitionally excluded). One theory is that the whole concept of "white" being the American default will break down if the amount of people (and property) covered is allowed to get too small.
Coined by racial sociologist Daniel J. Gil De Lamadrid, white
inflation theory emphasizes the role white inflation, or the gradual
increase in ethnicities considered white, plays in maintaining
whiteness as property. It argues that when an ethnic group
transitions from non-white to quasi-white, the boundary between racial
dominants and subordinates blurs, threatening the contrast value of
whiteness as property. To preserve the value of racialized property,
inflationary pressure pushes quasi-whites into whiteness.
White inflation works to maintain the property interest in whiteness
by ensuring that the boundary between racial dominants and racial
subordinates does not blur.
Now I don't know about all of that. I really haven't studied the research on Whiteness as much as the topic deserves.* However, it does seem like Franklin in particular didn't consider Germans to be "other". In 1732 a young Franklin even published the first German-language newspaper.
So it doesn't seem weird at all for a mid 40's Franklin to be viewing Englishmen, Scotsmen, and North Germans as "us" and everyone else as "them".
* - I guess I should warn the curious reader here that the entire concept of studying the history of whiteness and the social forces behind it (also known as Critical Race Theory) is enough to get one thrown out of some American political circles as an apostate. In many places in the USA, its actually illegal to teach. This is forbidden knowledge.