Okay, so how would one go about escalating the Franco-Prussian war into some sort of premature World War 1, or at least a conflict that spans across almost all of Europe? Assuming this is possible, what would such a conflict look like? How would it go? Who would be allied with the French, and who would be allied with the upstart Germans?

Yeah, I don't know what else to say. I think this is a pretty interesting idea (though I'll be the first to admit that I'm kind of biased), and I'd like to see what you guys think of it.
Austria is a contender imo to throw around in this era. The loss of territory to Prussia, plus the hegemony of Prussia over Germany could be a spark.
IOTL The British didn't directly join but still contested the war, if you want the biggest possible war, its possible?

What do you mean, they contested the war? They may have expressed unease after Frankfurt, but there's a vast gulf between that and actually doing something about it, especially during the Splendid Isolation period.
I think it's theoretically possible for a larger Franco-Prussian War (or whatever it might be called in this ATL), but I don't think it could get to the levels of WWI. And each country had its own possible motivations for joining or not.

If Leopold of Hohenzoller-Sigmaringen is crowned King of Spain, France would probably drag them into this mess, as Leopold's candidacy was the casus belli France and the German states went to war over and with Leopold on the Spanish throne, the French would be compelled to kick him off of it. In short, if Leopold becomes King of Spain, then Spain probably sides with Prussia. If the coronation is still averted, Spain probably stays neutral.

Denmark could be compelled into siding with France, because they wanted Schleswig-Holstein back, but unless France clearly beats Prussia and Denmark somehow obtains an actual casus belli, they're staying out of it.

Austria could be compelled to join France. Franz Josef wanted to side with the French in OTL, but was prevented by the Hungarians. If the Hungarians for some reason don't oppose war (which is unlikely) or Franz Josef is compelled to ignore them (which wouldn't be very smart on his part, something which he recognized) Austria probably joins France. If not, then Austria stays out of it, which is what happened.

The Russians could theoretically side with France, but why would they? The didn't have the hindsight to realize the fact that Germany would unify, and Bismarck was always sure to make Prussia/Germany stayed on Russia's good terms, and OTL it wasn't until he left office Russo-German relations soured, so for as long as he stays in office, Germany and Russia would get probably get along (although the minute he leaves office, Germany and Russia will very quickly be on opposing sides). Also, if Austria allies with France, Russia is not going to ally with them. After Austria refused to help Russia in the Crimean War, Austro-Russian relations were TERRIBLE at this point in time. They would rather see a unified Germany than ally with Austria. If Austria allies with France, Russia might actually ally with the Prussians, because they'd rather see a united Germany (which under Bismarck would be friendly to Russia) dominate central Europe than a Habsburg Austria to whom they are actively hostile to do the same. I've also heard of a secret anti-Austrian defensive alliance between Prussia and Russia in effect about this time, but I haven't been able to confirm it, so there's a chance Russia may be treaty-bound to support Prussia. IMO, Russia probably stays neutral or allies with Prussia, but only if Austria allies with France.

Without our 20/20 hindsight, Britain is not getting into this mess. This is the Era of Splendid Isolation, after all. I don't see how Britain would get involved in this. Best casus belli I can think of is somebody stepping on Belgium's toes in some sort of ill-advised proto-Schlieffen Plan, but this is 1870, not 1914. The geopolitics of the time are vastly different, and British neutrality is a near-certainty, IMO.

The Ottomans have their own problems. Unless Russia steps on their toes, they're not getting involved. Most I can see them doing is duking it out with Russia at the time, but only them. No one else is gonna bother with them except maybe Britain and/or France, but it seems very unlikely to me.

Italy might want things France has or wants, but they don't want to go to war with France. They might join the Germans if they fight against Austria, and an earlier invasion of the Papal States might warrant a response from Napoleon III, but I don't think Victor Emmanuel II wants to go there yet. I have an idea where a differing set of circumstances lead Giuseppe Garibaldi to use his wish for battle about this time to try to take Rome again rather than fight for France, which might lead to Italy accidentally provoking France, but it's not a very good idea. The point here being that Italy wants to stay on good terms with France but hates Austria, so they're like Russia: either neutral or potentially allying with the German states if Austria gets involved.

As for the result of this war, the side with Germany still probably wins, as the expansion of the war would likely see more support come in for them than for France. In fact, they may get to annex a large portion of Austria, which would make them much more powerful in the long-term. Spain as an ally of Germany might be cemented in this war, as could theoretically an alliance with Italy. Hungary might come into existence as an independent kingdom if Austria is partitioned (though I'd imagine Bismarck would fight this with tooth and nail, because he would not want Austria as part of Germany).
Austria could be compelled to join France
Dout it, post ausgleich Translethia wanted peace to magyazer their land and after 1866 the last thing Austria could even afford is fight again their northern cousins, as ironically their own germans would rebel vs the Hasburgs
The timeline in my signature may have information of interest. I was planning on having the war escalate into something like this but sadly haven't had the time.
If Russia fight on side of Prussia what land could Russia get? And how can it affect Russian-Turkish war of 1978?
Russia was kinda pushed to Neutrality due to shrewd diplomacy on the Prussian side, but England is a contender.
There was no need in a “screwed diplomacy”: after the CW Russia and Prussia were naturally friendly and by the time of the FPW NIII spoiled relations with Russia over the Polish issue.
If Russia fight on side of Prussia what land could Russia get? And how can it affect Russian-Turkish war of 1978?
Against whom would it be fighting? Prussia was doing just fine against France on her own (with the German states on her side) and AH was not suicidal enough to get into war on the French side with a hostile (after the CW) Russia at her rear.
Against whom would it be fighting? Prussia was doing just fine against France on her own (with the German states on her side) and AH was not suicidal enough to get into war on the French side with a hostile (after the CW) Russia at her rear.
I was assuming Austria-Hungary is on side of French like some people mention above.
All I think you'd really need to do would be to have the Austrians go to war with the Germans - easier said than done I understand, though a big help would be to not have Beust as the Austro-Hungarian Foreign minister. The Russians IOTL offered the Prussians their support if Austria joined the war, if that did happen then I can't really see Britain staying out of the war, especially as IMO the Austrians would fare pretty badly in such a scenario with likely Hungarian rebellions springing up in protest against Vienna ignoring Budapest's wishes a mere four years after the 1867 Compromise. The last thing Britain would want is Austria-Hungary knocked out as a major player on the continent as well as France being brought down a peg or two.
I was assuming Austria-Hungary is on side of French like some people mention above.
IMO, chance would be extremely small. Peace after the Austrians-Prussian War was quite generous and France was not a “traditional friend”, to put it mildly. Neither was Italy. Russia was friendly with Prussia, on bad terms with France and did not have a single reason not to join Prussia against Austria even if Milutin’s military reforms were not complete. Plus AH could have internal problems: now it needed an agreement of both its parts.
In order to escalate this war, Austria needs to join France. Without this, the war at most can involve three countries (France vs Spain and Prussia/German states). Emperor Franz Josef wanted to join the war but was prevented by the Hungarians. To me, the most plausible way to escalate this war is to reduce Hungarian influence in Austria. Otherwise they'll block Franz Josef's attempts to declare war, which prevents the war from escalating. Only other option is to make Franz Josef ignore the Hungarians, which Franz Josef is not going to do because that would be a very dumb idea. I don't know enough about AH's internal politics at the time to guess how the former option (which is the only plausible option, IMO) would occur, though (different/no Ausgleich?). If Franz Josef does declare war, then the war is much more likely to escalate.