Good question. I never really thought about that. As Ahmadi pointed out, in structure "a" you are using plural nouns but in structure "b" you are using adjectives to take the place of nouns. I think if the singular noun is the same as the adjective, then you make it plural. So really, the pattern would be: a1) As the Italians say ... a2) As the Germans say ... a3) As the Englishmen say... or b1) As the Italian people say... Of course, "Englishmen" excludes English women, so it is not equivalent.

For forms (b), instead of using the plural form, you can use the adjective "British" or "French" to refer to the people or culture of those countries. Here are some examples: "As the British say, keep calm and carry on." "As the French say, vive la différence." Alternatively, you can use the demonym or the nationality to refer to the people of those countries, for example: "As the English say, an apple a day keeps the doctor away." "As the French say, joie de vivre." Note that while the terms "English" and "French" are sometimes used as nouns to refer to the people of those countries, it is more common and polite to use them as adjectives.

What an interesting question. I suspect that this pattern can be traced directly to the French. (For the impact of French on English, see the Norman Conquest.) In French, you have "un Italien" (an Italian) and "un Allemand" (a German) but "les Italiens" (Italians) and "les Allemands" (Germans). In both French and English, -s is added to form the plural. But the situation changes for "un Anglais" (an Englishman) and "un Français" (a Frenchman or a French person). These words already end in -s, so the plurals don't add another one. In English, this pattern, when borrowed, led directly to "the English" and "the French." This isn't as odd as it seems. Irregular plurals of this type -- with identical singular and plural forms not ending in -s -- already existed in Germanic languages. A few of these words still exist today: one sheep/two sheep, one fish/two fish, one deer/two deer.

For b1), "As the English say..." For b2), "As the French say..." I can't explain it, except to say that I guess "Italian" and "German" are countable nouns, but "English" and "French" are non-countable. I'm just reviewing words in my head, trying to figure out of there are any rules, and it seems to me that demonyms ending in -ch, -sh, and -ese are used as if they are noncountable. Perhaps it is a question of euphony, as it would be difficult to add an -s sound after these endings. "Why did the Scots want a Stuart on the throne?" "The Venezuelans won freedom from Spain in 1819." but "The Welsh are known for their singing because of the rich musical tradition in Wales..." "The Danish are proud of their dairy products." "The Chinese developed gunpowder around the year 1000 CE."

6