How did enlightenment ideas influence modern beliefs about the importance of education?

As to how they influenced education:
Both Montesquieu and Voltaire liked the idea of a despotic king ruling in a Enlightened Absolutism, which meant that the king would be influenced by the enlightenment and support it with education, free press, freedom of speech, science etc, and embrace reason.

This was meant to be spread throughout the country, to everyone.It was only meant to teach people how to read, but many paid the teachers to teach them how to do maths and also write.
An example of a modern belief that spans from enlightenment ideas is that education should be free and available to anyone, as seen in numerous countries of the European Union.
hope it helps