Ruskin at MP I:90, MP I:227, MP I:280, MP I:379 appears to define Claude and both Gaspar Poussin and Nicholas Poussin as Italian painters. Waagen in a letter dated 15 May 1835 published in Waagen, Treasures of Art in Great Britain, I, p. 17, defined Claude and Gaspar Poussin as Italian, but refers to Nicholas Poussin as French; no reasons are given there for the categorisation.
In the Dulwich Gallery paintings by Claude, the Poussins and Salvator Rosa were hung together in Room 4. At the time when Ruskin was writing the National Gallery was not hung according to 'schools'; the later hanging by schools followed political rather than stylistic divisions so that Claude and the Poussins were categorised as members of the French school.
J. D. Harding, Ruskin 's drawing teacher, had a firm view on this:
When speaking of the Italian school, I do not mean Italians only, but the painters of Spain, France, and of our own country, who adopted the same kind of imitation as theirs (see Harding, The Principles and Practice of Art p. 21).
The uncertainties are perhaps unsurprising in a period of what Bagehot called 'nation-making' when the nature of 'nation states' was a central and unresolved political question.