Branching, Premodifiers, and Postmodifiers
I believe that what you are looking for here is whether a particular structure, in this case a noun phrase, should happen to be a left-branching structure or a right-branching one. English does indeed have both kinds, but there are rules about which ones go where: adjectives to the left, phrases to the right.
With left-branching structures, the head of that structure comes at the very end, and things modifying its head come “before” it. Consider a noun phrase such as this one:
My little brother’s three favorite toy fire trucks
That structure is left-branching and head-final because all the modifiers of the head noun truck occur to its left. In an English noun phrase, all determiners — like articles, demonstratives, possessives, quantifiers, and numbers — along with almost all adjectives necessarily precede their head noun. The Wikipedia article on noun phrases states this as follows:
The allowability, form, and position of these elements depend on the syntax of the language in question. In English, determiners, adjectives (and some adjective phrases) and noun modifiers precede the head noun, whereas the heavier units – phrases and clauses – generally follow it. This is part of a strong tendency in English to place heavier constituents to the right, making English more of a head-initial language. Head-final languages (e.g. Japanese and Turkish) are more likely to place all modifiers before the head noun. Other languages, such as French, often place even single-word adjectives after the noun.
Furthermore, when you have more than one adjective in a noun phrase, those adjectives must be arranged in a particular order, an order that will not be obvious to non-native speakers from languages very different from English. (Remember the end of the previous sentence: I’ll return to it.)
In the larger scope of things than just premodifiers of head nouns, English is more of a right-branching (head-initial) language than it is a left-branching (head-final) one. I’m not talking just about noun phrases now but the sentence structure itself. The direct object falls to the right of its verb, for example, and prepositional phrases that modify nouns must come after that noun.
That’s why you have a hole in the wall, not an in-the-wall hole. You also do not normally “a hole in the wall have”, either, because putting the object before the verb in English is to draw special attention to it. It is not unheard of, but unlike in today’s Dutch or German, in today’s English this practice is rare enough that it can surprise some readers. Putting the object first doth many an archaic(‑sounding) sentence make, and all that jazz. :)
Prepositions on the left?
The only prepositional phrases that modify a head noun but come before it instead of after it are when they are involved in predeterminers such as both of, some of, many of, lots of, a lot of, a number of, a handful of, half of, half a dozen of, and all the rest like those. That’s why we say:
A lot of these problems are easily avoided.
There “a lot of” is something of a decoy, because the of there looks like the start of a prepositional phrase branching right from lot. These quantifying predeterminers are in the position before the determiner slot in a noun phrase; they do not change what the actual head noun is. It’s still a quantifier whether it’s many or whether it’s a lot of. The lot in the quantifier is not the head. Instead, the actual head noun is still problems in the example give above. If the head noun were lot, it would have to be lot is avoided; but it isn’t. It’s still problems, which is why you still have a plural verb there.
This sort of construction with its decoy of can be confusing to non-native speakers — and sometimes even to native ones who think about it too hard. :) Since they are left-branching and not right-branching, they work like adjectives and not like normal right-branching prepositional phrases. I like to think of this sort of quantifier as a “partitive determiner”, but as far as I know, I’m the only one who does that.
“Heavier elements to the right”
But those sorts of prepositional premodifiers are the exception. Normally prepositional phrases are postmodifiers to the noun phrase. So while postpositive adjectives are the exception, with phrases postpositive positioning is the rule not the exception.
In the same way that prepositional phrases that modify a noun must ordinarily follow it, so too must any verbal phrases that modify it also come after their head noun. This includes participial phrases like “people running for president”, infinitive phrases like “problems to avoid”, and dependent clauses like “screams which are seldom heard in these parts”. Those are all right-branching and head-initial structures.
So earlier when I said “languages very different from English”, I was intentionally using a right-branching structure to modify languages. That’s really a reduced clause under something called whiz-deletion. The wh- word plus the inflected form of the verb be like are or is are both deleted (hence the term whiz-deletion), leaving just an apparently postmodifying adjective behind. But it is actually a clause, and clauses have to come afterwards. The real structure is
languages [which are] very different from English
So phrases that modify a head noun must follow it in English, including these sometimes-disguised clauses like the one I just showed you.
A few more odds and ends
With verbs, it is not always that way, in that an adverbial prepositional phrase can precede the verb. Sometimes this triggers subject–verb inversion, like here:
In the cupboard stand four jars of jam just waiting to be eaten.
You mention the Latinate languages like French being different from English in this. For the most part, you are correct. However, Romance languages normally put determiners to the left just like English, even though their adjectives usually go on the right.
There is an exception to this Romance tendency to use postmodifying adjectives, though. Certain very common ones like big, little, new, young, old, good normally go to the left in Romance, being descriptive not restrictive. The restrictive adjectives go to the right.
And even in Romance they can use those common adjectives as postmodifiers to make them restrictive instead. They do this when they want to draw attention to the common adjective, the way we in English use stress in our voice to distinguish our pretty wife from our pretty wife. In Romance, you would flip the “pretty” part to effect the same thing. So Spanish mi bonita esposa is my pretty wife but mi esposa bonita is my pretty wife. See the difference?
But you’re mostly right: normally Romance wants its adjectives to come after the nouns they modify, which is just the opposite of how English usually arranges them.
Germanic languages (mostly) like to put their adjectives first, while Romance languages (mostly) like to put theirs afterwards. So the Germanic order gives us general counsels while the Romance one produces attorneys general. But postmodifying adjectives (not phrases, just adjectives), are comparatively rare in English, with well-known exceptions like galore, extraordinaire, and the occasional proper occurring postpositively.