I’m sure we’ve all had a laugh at hearing someone say ‘Would you like that with au jus?’. (‘Au jus’ means ‘with [its own] juices’, so ‘with au jus’ is redundant.)
What is the correct formation in English? I would think, ‘Would you like that au jus?’ Suppose you want extra juices? ‘May I have some more jus?’ I wouldn’t ask for ‘more au jus’.
I don’t need an answer fast. The question of usage hasn’t come up for me. Just curious.
I just call it ‘ow juice’. I don’t see the point of using non-english phrases in their native context.* Au jus* has become a noun in English, that’s the way we roll.
TriPolar is right.
The “correct formation in English” is exactly how people use it in English. That is, to mean the sauce itself and not as a phrase that means “with juice.”
We rip words from other languages and bend them to our will all the time. Nothing unusual.
I took French in college, so hearing “with au jus” is quite grating to me. I try to say just “jus” (pronounced jew) but usually people don’t know what I’m talking about. They need to hear the au in order to parse it.
“With au jus” is wrong, and I don’t care if it’s a loan word. If we want "au jus to be one word, then stop spelling it as two-- hyphenate it, or something. It’s pretentious, and we just should have said “juice on the side” to begin with, but if we are going to say “au jus,” we should get it right.
This is a good question. I tend to go back and forth between “with jus” and “with au jus” pronounced as “oh zhoo.” Most people say “au jus,” so, while I know French, in the interest of communication, I’ll ask for more “au jus,” say, instead of just “jus.” I’ll write “jus” on these boards because I know people will understand me and I don’t have to deal with someone pedantically pointing out that “with au jus” is redundant/illogical/“incorrect” or some b.s. like that. I file it away with phrases like “the hoi polloi,” “ATM machine,” and “the La Brea Tar Pits,” as, perhaps a little redundant if one is being hyperliteral, but not in natural speech.
The correct formulation is the one that will most easily accurately convey the necessary information to the listener.
Personally, I just say au jus for everything. As with so many words and phrases, it doubles as an acid test. If someone gets upset or supercilious about it, I know not to waste any more time with them.
Sorry excuse for a stickler, Inner Stickler seems to be.
That’s like the 3rd time this year. Maybe I really do need to change my username.
We don’t have a single word in English that accurately denotes the particular liquid involved. “Juice” and “gravy” usually bring something else to mind, and asking for one of them will usually result in confusion and having to explain. “Jus” is not an English word and the meaning will not be understood by the great majority of English speakers. As mentioned, “au jus” has become established in English as a noun phrase that conveys the exact meaning to virtually everyone. If it’s more important to you to preserve French grammar in an English-speaking country than to get served the stuff you want then protest all you want, but don’t be surprised if you waste a lot time getting nowhere.
Au beaucoup jus, s’il vous plait.
I know, I’ve often wondered about the username myself. 
I should actually amend my post to say that I normally will say “I’ll have a roast beef au jus” instead of “I’ll have a roast beef with au jus,” (at least I think that’s how I’d say it) but I, if I want extra, I will say “roast beef with extra au jus” or similar. Plainly referring it to jus, I think would be confusing for a lot of people.
One where I really get tongue-tied over is bruschetta. I want to say broo-sketta, but most people say broo-shetta, but every so often I find a waitron who does repeat it back as broo-sketta when I go for the popular broo-shetta pronunciation, but I’ve also had an issue with servers being momentarily confused by broo-sketta. So now I just order crostini instead. 
Au, jus’ fergedabouddit already.
I’ve never heard people say “with au jus,” but I have heard “au jus” treated as the name for the sauce. “Would you like some au jus with that?” “I’d like some extra au jus,” etc. Au jus is still an adjective when used with an actual dish, but has also taken on a noun form.
I’ve also never heard anyone say “ow juice.” They say either “oh zhoo” (a la français) or “oh jew.” I still prefer the first version.
Gesundheit.
Anyhow, I say, “I’d like the roast beef, au jus on the side.” That parses just fine, and it ensures I get it in a cup because some places dip the whole thing or ladle it over the sandwich served on a deep plate.
Look, if I had known Indistinguishable would be so damn persuasive, I’d have chosen a different name.
I just say broo? and wait for them to helpfully supply shetta or sketta and then that’s what I use for the night.
Meh… the problem is that au jus has come to have two different meanings: originally a style of serving roast beef, it has also come to mean a separately prepared, and often separately served, thin gravy-like concoction that is itself referred to as au jus.
I think the next time you’re out you should go back to ordering broo-sketta. And once you have that sorted out, and the waiter creature wants to know what you want to drink, order a Caesar. 
I’ve certainly seen it on menus. If you google "menu ‘beef with au jus’ " you can find some examples of it. For example here: “Roast Beef with Au Jus and Cheez Whiz.” Or here (PDF): “Homemade Italian Roast Beef (with Au Jus).”
I ask for my French Dip sandwich au gentile. I want the whole sandwich, not 95% of it!