If we were to say the school in French, we would say:
L'école
The apostrophe is commonly taught to come so that vowels don't come close to each other. If we were to say 'a school' it would be:
une école
Why is it fine for vowels to come close with indefinite articles but not definite articles in French? Can this be traced back to historical reasons?
The apostrophe is commonly taught to come so that vowels don't come close to each other.
This is not stated precisely, and you might be misunderstanding. The apostrophe is a consequence of the pronunciation. What happens in French is that in some cases, two vowel sounds can't be next to each other, so the first one is removed. The apostrophe is used to replace a letter, if the usual word includes a letter with the vowel sounds.
French has many one-syllable words pronounced with a consonant followed by the vowel [ə] (schwa sound). Their spelling ends with the letter e. These words include le, de, me, te, se, que, etc. When one of these words is followed by a word that begins with a vowel sound, the [ə] sound is omitted, so the first word only contributes a consonant sound. This is reflected in the spelling by replacing the e with an apostrophe. This also applies to a few other cases, in particular la (feminine of le). For example:
In words that end with e and that have another vowel, the final e is normally silent (“E muet”). Since the presence of a vowel at the start of the next word doesn't (much) change how the two words are pronounced, there is no need for a change in the spelling either².
(There is one exception: in compound words where the second part is que (lorsque, puisque, etc. — not chaque where the final -que is just a coincidence), the e is elided even though it isn't normally sounded, e.g. jusque + à → jusqu'à ([ʒys.k] + [a] → [ʒys.ka])).
¹ It actually affects the syllable boundaries: a trailing consonant sound from the first word moves to the beginning of the next word if the next word starts with a vowel. But this is not reflected in the spelling.
² There are dialects where the “E muet” is actually sounded, but the spelling rule doesn't follow these dialects.
This use of the apostrophe goes back to Old French, at a point when the final /ə/ of any word was always pronounced, unless it was followed by a vowel, in which case it was systematically elided.
In this respect, this means that le (and any other word used with the apostrophe, like se, que, je, si, de, la or (at the time) ma or sa) would have had the exact same behaviour than une (or any other words that doesn't vary orthographically whether followed by a vowel, a consonant or nothing, like cette, grande, elle or certaine). So any explanation relying on phonology seems suspect or a post facto rationalisation.
There is, however, one factor that unites all the words that show orthographic elision: they're monosyllabic (excepted compounds ending in que, that would have at first been written in a single word). Their lost vowel is their sole vowel, and they end up relying on the following word to exist. By contrast, une is more recognisable as its own unit even when followed by a vowel, since it keeps at least one syllable. This means that there was a reason to write those monosyllabic words as a unit with the word they leant on, with the apostrophe serving as a boundary between the two morphemes, while leaving polysyllabic words separate, even those like elle or une that were also clitic in nature.
In modern French, it makes a bit less sense, since said rule of /ə/ elision before a vowel isn't active anymore, and we drop /ə/ in short monosyllabic morphemes that are dependant on the following word all the time even when said word starts with a vowel. But French orthography isn't made for modern French, but for its long dead progenitor, so such inadequacies are commonplace and inevitable.
The simple reason is that in "le" the e is not silent, whereas in "une" the e is silent e.
le [lə]
une [yn]
The apostrophe's aren't simply "used", they are used for a purpose.
In French, as in English, apostrophes can be used to indicate that some letters have been omitted. For instance:
In the case of "une école", when people speak they don't drop the "e_" and say "un'école"; the barely pronounced "e" at the end of "une" naturally merges with the "é" without having to remove it. And if anyone ever did drop the "e", it would sound wrong: the article has changed gender and no longer agrees with the noun.
Consider "un ami" and "une amie", and why "un'amie" would be wrong.
The purpose of the elision between two words is to avoid a hiatus. There's no hiatus in une école since it is pronounced [yne'kɔl], the final e in une is not sounded.
une ends with a vowel graphically, but it actually ends with a consonant (that is its sound ends with a consonant - the point already made by @LPH in their answer). This is similar to how some English speakers put an in front of any noun beginning with a vowel in spelling, although not all these nouns actually begin with a vowel. I am not a native English speaker to say that it is completely wrong (and I ahve seen it done in books and scientific papers), but I can't stop from shivering every time I see something like an union, although I think it is perfectly appropriate, e.g., in an urge where n comes between two vowel sounds.
Remark:
An example encountered today in another community: "a N-body quantum system" vs. "an N-body quantum system". Here we have "consonant" letter N, which is actually pronounced with a vowel sound: [ɛn].
