Grammaticality – Use of ‘The Better’ Explained

Disclamer: English isn't my first language.

I learned during my English courses (a few years ago), that there is, as in French (which is my first language), a comparative and superlative version for each adjective. And for the adjective good it goes like this:

good, better, best

The thing is, when I listen to different English people speaking (videos on YouTube, conferences, etc.) I often hear something like

the better solution is…

This doesn't translate well in French (actually, if you translate the word as is, it's a huge grammar error) and most of the time I thought it was just the speaker making a mistake (which could be considered as not that important in English). Instead I would expect either

• the best solution is… [superlative]
• a better solution is… [comparative]

and not the use of a comparative as a superlative.

But recently I've started to listen to a course from Shelly Kagan, a professor of philosophy in Yale University, who seems to use this same construction.

Now, I wonder if what I was taught wasn't completely correct and indeed "the better solution is…" is correct, or if professor Kagan, and everybody I heard saying that, is making a mistake (of course this doesn't affect the quality of the content or the skills of the speaker).

If it is indeed a mistake, is it considered as an obvious one, or is it not that noticeable?