Adam Smith wrote an interesting section of The Wealth of Nations on the issue of education. It appears in Book V of the volume, which is the book where he begins to qualify his otherwise laissez faire position. The section "Education of Youth" is Chapter 1, Part III, Article II.

Most of the section is devoted to explaining why endowing public money for educational institutions has a negative effect on the quality of teaching. Most of the arguments should be familiar to anyone who follows debates about public education, teachers unions, etc. It's pretty clear that Smith thinks full public funding for education will produce a negative outcome.

However, he does then start to make a critique of a society lacking any education or virtues—one that's actually quite similar to the critiques Tocqueville and Nietzsche would make decades later. Talking about the effect of the functional division of labor on the populace he writes:

But the understandings of the greater part of men are necessarily formed by their ordinary employments. The man whose whole life is spent in performing a few simple operations, of which the effects too are, perhaps, always the same, or very nearly the same, has no occasion to exert his understanding, or to exercise his invention in finding out expedients for removing difficulties which never occur. He naturally loses, therefore, the habit of such exertion, and generally becomes as stupid and ignorant as it is possible for a human creature to become. The torpor of his mind renders him, not only incapable of relishing or bearing a part in any rational conversation, but of conceiving any generous, noble, or tender sentiment, and consequently of forming any just judgment concerning many even of the ordinary duties of private life.
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His dexterity at his own particular trade seems, in this manner, to be acquired at the expense of his intellectual, social, and martial virtues. But in every improved and civilized society this is the state into which the laboring poor, that is, the great body of people, must necessarily fall, unless the government takes some pains to prevent it.

He goes on to write a justification for the public funding of the education of the poor. The state should teach the Three R's by establishing parish schools, giving prizes for academic achievement, and requiring students to pass exams before entering a trade. In this way, he writes:

The more they are instructed, the less liable they are to the delusions of [religious] enthusiasm and superstition, which, among ignorant nations, frequently occasion the most dreadful disorders. An instructed and intelligent people besides, are always more decent and orderly than an ignorant and stupid one. They feel themselves, each individually more respectable, and more likely to obtain the respect of their lawful superiors, and they are therefore more disposed to respect those superiors. They are more disposed to examine, and more capable of seeing through, the interested complaints of faction and sedition, and they are, upon that account, less apt to be misled into any wanton or unnecessary opposition to the measures of government.

You should keep in mind that Smith is justifying only public funding for the education of poor youth, not general funding for the education of all at all levels. Nevertheless, even Smith saw areas in which laissez faire needn't be strictly followed, and which could benefit society if the government were to intervene.