So there is every chance this is going to go on for a while, but, sure. Let's do it.
Whenever I'm trying to uncover a language used in an already-existing IP, the first step could be considered a little boring. It's the research phase; before worrying about grammar or alphabets, I read up on as many words as exist in the target language. Noxus doesn't have many. Here's a quick checklist I run through along with specific examples from Noxian:
1) Names -- while there are plenty of names in every language with no semantic meaning (James, Cathy), the majority of names will use the standard phonemes, giving you an idea of the breadth of consonants and vowels. Because of, as you identified, patronymics like "Le Blanc" and "du Couteau" we know that those names are untranslated, fixing "le" and "du" as some sort of articles.
2) Proper nouns -- although nearly all of the lore (to be fair, all of the lore I could find, but I'm not discounting the possibility there is something I missed) translates non-common words to the English-equivalent, proper nouns often give away a title or phrase in the target language. For example, we know that Swain is or wants to be Grand General of Noxus. Assuming there is a Noxian language, it stands to reason that there is a Noxian equivalent to Grand General (otherwise that wouldn't have been the translation).
3) Nouns -- the same as with proper nouns, although I haven't found as many Noxian nouns. We know there is a noun which means "quick move," or some approximation thereof, since Katarina uses "shunpo," a non-English word, as a noun. Whatever word it is, it can't have a good English equivalent, so we can re-create it once we've set up more of the Noxian tongue.
Moving on to grammar, remember those fixed morphemes we identified in the names? Those are definite articles, which is our first clue to deciphering Noxian syntax.
As a romantic language, Noxian would likely have tenses and verb conjugations, formal and informal constructions, as well as at least twenty characters in its alphabet. The existence of both [v] and [u] is problematic in a way, since a simpler alphabet is easier to asterisk. But with [i] and [y] both dropping in as well, we have to assume we're dealing with at least 24. The proposed alphabet looks like this:
*a, b,c, d, e, g, h, i, j, k, l, m, n, o, p, r, s, t, u, v, w, x, y, z
(using [ph], for example--we haven't found any Noxian words that need an f, nor any good reason to have it around)
We can assume, from the stories we know, and the brief snippets of dialogue we have between Noxian characters, that there are two forms of Noxian. One formal, one informal. Let's also assume the formal version would be used in most political or judicial situations.
Based on the power dynamics on display in Noxian culture, I decided to assume that the formal version would be less comfortable for the average Noxian to speak. Once I decided that, it was easy enough to determine that ornate, descriptive prose with a flowing rhythm and soft vowel closings would not be the average Noxian's cup of tea. Thus, formal Noxian words end always with a vowel, where gutter Noxian or informal Noxian can end with either a vowel or a consonant, although never with the [ee] sound as used only in formal diction.
There are even subtler distinctions. [Ch] pronounced as [kay], as in Jericho, occurs only in formal Noxian. In informal Noxian, the [kay] sound is always represented by the [k] letter. From this, you should be picking up that Noxian is different from the formal and informal forms of most romantic languages. For all intents, Noxian is actually two completely separate languages, which I determined because of an inchoate conflict I've pieced together, where the nobility (who frequently use formal Noxian) and the military (comprised largely of non-noble Noxians using informal language) have grown further and further apart over centuries of arguments and dissent.
The Noxian Articles and Slight Variations:
Le -- the, informal
Du -- the, formal
Ka -- a, informal
Ke -- some (as an article, informal)
I -- a, formal
Ai -- an, formal
En -- an, informal
Noxian words and phrases I've used so far --
"Na kalyn" --"by the raven", informal Noxian. The formal version would be "ni kali". Here Anton is purposefully baiting Katarina, using gutter slang.
"docherni" -- Remember that this is pronounced "dough-KER-ni". It's actually an honorific, as Anton is trying to appeal to Kat's noble side. An English near-cognate, docherni means "Revered Daughter".
"druz'yami" -- Here's where we go uber-deep. This is a portmanteau of sorts, the kind of slurring that happens when a common suffix melts over the rest of the word. The full phrase would be "druz a du yami" or "a fight to the next level". "Druz" the noun form of the verb "fight". "A" means "to". "Du yami" could be "the top" or literally [ya] + [mi]"above me" but there's probably no reason to break up a word like that unnecessarily, so when combined with a Noxian tradition of formal duels to the death, "next level" describes rising to the occasion with a subtext of ascending from this world (or descending, we haven't examined that yet). You should recognize that this is a formal phrase, a well-worn cliché for instigating a duel.
"malen'mal'chik" -- Another one of those contracted phrases. Let's take a step back to why so many contractions? We can extrapolate from Draven and Darius's behavior, as well as Talon, Katarina, and Cassiopeia's impulsiveness, combined with the notion of a society governed by a culture of power, and the language would likely be gruff, workmanlike, as terse as possible in its informal version. Formal Noxian probably tends the other way, with flowery ornamentations and rhetorical flourishes. Remember that informal Noxian ends in consonants and occasionally vowels, while the formal version only ends in "[i], [e], [u], [o], and sometimes [a] or [y]". We can assume, since Noxian is a phonetic language, that "mal" is the root of the word "malen". It's even easier in this case, since the full phrase is "malen maleninichik," or "very stupid very stupid person." Literally, "bad brained boymanchild with a bad brain." Where "inichik" tells us that we're talking about a "inchik/boy child" who is older than he should be--that interjecting [i]--possessing of the prefix ("bad brained" or "stupid").
"Direya" -- The suffix [-eya] is attached to a noun to signify "little girl" or "daughter". "Dir" in this case would be "street". I'm pretty sure you can figure out the word from that.
"Kreshnaya" -- "Shadow mother". An unofficial term of address for one of the graduated assassins of the Sinister Blade. Can be used as a curse or pejoratively, as Marcus uses it here. Well, somewhat pejoratively, I think it's possible to detect just a little bit of begrudging respect.
"Nikiya" -- Just as "eya" means "little girl" or "daughter", "iya" is "wife" or "sister" (for those wondering, "aya" would be mother or grandmother). "Nikiya" is a term of endearment, where "nik" is "cute" and the full word translates as "cutie" or "little cutie." As you can undoubtedly imagine, almost every diminutive used with young women is unfortunately used as a pejorative when said to a man. It's worth pointing out that the same is true in reverse, describing or addressing a woman using the diminutives meant for boys would suggest weakness or a lack of power in the subject.
"Dai luta" -- "May you die with blood on your hands" or "Die in battle" or "Die bleeding". Traditional Noxian salute between soldiers.