Dans ici s’intégrerait trop facilement une critique de notre enseignement, facilement signifie aisément. Mais deux interprétations sont possibles. Dans les deux cas, j’assume que notre enseignement signifie simplement l’école en France, qui n’enseigne pas ce qu’il faudrait sur le Canada (d’après la phrase précédente).

La première interprétation est tout simplement que l’auteur dit qu’il est très facile de critiquer l’enseignement, qui ne fait pas ce qu’il faut, bien entendu. Ici aisément veut dire que ce serait facile, car les problèmes de l’enseignement sont évidents et bien connus.

Mais (sans doute pas ici) il pourrait aussi y avoir une autre interprétation, presque péjorative, du mot facilement. Une critique facile signifie une critique vulgaire, basse: l’auteur de la critique n’avait pas beaucoup de substance pour sa critique et a donc eu recours aux arguments les plus faciles, les plus bas. Peut-être quelque chose qui est dans l’air du temps, que tout le monde croit, mais qui n’est pas forcément vrai.

Sans raison valable serait possible dans la première interprétation. La première interprétation est sans doute la plus probable, vu ce qui précède dans le texte.

• De quelle œuvre le général de Gaulle tire-t-il sa citation de Paul Valéry et sa conclusion suit-elle directement le passage qui précède dans l’œuvre originale ?

I’m afraid there is no way to answer to that question yet using on line resources. After searching Paul Valery’s writings, it seems de Gaulle quoted a document that is not yet scanned / indexed by the usual search engines or Gallica.

The excerpt de Gaulle used is certainly from Paul Valery’s cahiers. These are notebooks he was writing to every morning and there are 260 of them. That’s a big amount of text that was only partially published.

These cahiers recently entered into the public domain (in 2016 after a 70 years delay) so there should be a way in the future to retrieve them on line and finally find the original text. This page from the OBVIL (Sorbonne) is describing a project aimed to make them available but there is no recent update.

Regarding the part of your question concerning “De quelle œuvre” and whether the final quoted sentence (or “conclusion” as General de Gaulle called it) immediately followed the preceding quoted passage in the original, I agree with this answer that it was from one of Paul Valéry’s as yet un-digitized/unsearchable journals/notebooks/cahiers.

Granted, Valéry did write very many personal letters of which, I’m guessing, at least some have yet to be published and/or digitized, therefore making one of them a possible source of the quote.

However, I can’t help but reading that final sentence as a sort of an undeveloped aside (directly related to/aimed at the preceding sentence) or even as a parenthetical note or reminder to himself or future editors that:

Here, a critique of our education would/could be [trop = “too” or
perhaps very?] easily inserted/integrated ^^(please see my own “aside” at the bottom).

(= “This would be a good place to insert/integrate^^ a discussion about the state of French (our) education as it relates specifically to why, as mentioned above, “our” knowledge/awareness of Canada/Québec is for the most part “vague” and of a summary nature.”)

Viewing this last sentence as an undeveloped aside/note/reminder as I do provides me with an additional clue, probably unnecessary, that the words did come from one of Valéry’s notebooks, perhaps his last, and that they were written in the exact order presented by the General.

Making such asides and/or notes to oneself would, in my opinion, be consistent with the general style of journal/notebook writing and perhaps even Valéry’s style in particular in light of Wikipedia’s claim that Valéry’s notebooks contained graphic indications, probably intended to facilitate their consolidation into one work or several future ones (= “des indications graphiques, probablement destinées à faciliter leur regroupement en un seul ouvrage ou en des ouvrages ultérieurs”).

(Please note, however, that my view does require me to interpret the General’s use of “Et Paul Valéry concluait” to mean “he finished his words/entry with” and not “he drew the following conclusion,” which interpretation might be contrary to what the General actually meant by those words)

[Trop] Facilement = ?

Viewing that last sentence as an undeveloped aside/note/reminder also “requires” me to interpret not only the appropriate sense of “facilement” to be “aisément,” but also the sense of “trop” used here as being (without the notion of excess) synonymous with “très,” as alluded to above where I put “very” in bold.

Without these two specific interpretations of “facilement” and especially “trop,” I cannot escape the feeling that “trop facilement” could nearly always be subject to being interpreted in its “sans raison valable” sense, if not [almost] by the fully negative, “without cause/unjustified” sense of the English word “gratuitously,” and in my opinion, neither of these senses would fit with Valéry’s last sentence, especially as I interpret it and its purpose.

Notre enseignement = ?

Concerning the meaning of “notre enseignement,” it probably stands for “the French education[al] system” as a whole, especially as it relates to teaching about Canada/Québec, but I believe it could also mean “what we as individuals have learned/know about Canada/Québec, regardless of the source of that knowledge” (kind of in the sense of Reverso‘s “leçon tirée de l’expérience” meaning of the word).

^^Finally, as my own aside, you will note that I use “inserted/integrated” in two places above instead of just “integrated” because although the General clearly used the word «s’intégrerait» at the press conference (at 60:45 on the video), there are written accounts (10th paragraph from the bottom) using, without further explanation, «s’insérerait» instead, including the linked one from charles-de-gaulle.org.

If that change was deemed justifiable for the sake of accuracy, it could have been made by someone who was more familiar than the General with Valéry’s actual words but who was too afraid or too respectful of the General to call express attention to his misquote.

Until the original becomes available, however, this is obviously just conjecture on my part and I must admit that I mention this “discrepancy” primarily to note (granted, with my limited ability to fully understand the difference, if any, between these two French verbs as used here) that «s’insérerait» somehow makes it easier for me to argue that the last sentence was originally intended as a note or reminder from Valéry to himself or future editors to “insert,” later on, something “here” about French/our education.