Leopold's candidacy was already dead in the water before the war started (the opportunity for Bismarck was created by de Gramont with his insistence that any future Hohenzollern candidacy to the Spanish throne had to be formally renounced by the king of Prussia), so it would not be any diplomatic "victory".The status quo ante bellum would be the most that the French could hope, but I expect further concessions. A partial demilitarization of the border is not excluded and a compensation is likely (but not a problem since the state treasury was full thanks to Magne, and given how quickly France was able to repay it IOTL). Otherwise, France has been humiliated and German unity de facto, soon to become de jure, has been realized around Prussia during that ''war of French agression''.
As for Spain , the situation doesn't much as Leopold's candidacy vaporates with the outbreak of the war. That could be the only diplomatic victory of France, but at a terrible cost.
The other points may work (I'm still convinced that the demolition of at least the fortress of Strasbourg would have to be conceded).
I'm not sure how the practicalities of a cease fire (even before the negotiation of a peace treaty) would be agreed though.
I suppose that the best way might be through the diplomatic good offices of Austria and Italy, assuming that the army of Metz has not been trapped and the Prussians at least slow down operations (Bismarck would certainly see the benefit of a quick peace, but there would be some kind of opposition from the army - if not from the king - and from the pan-German nationalists. Similar resistance to a peace treaty which effectively recognizes a French defeat would also be present on the French side. It's the reason for which I'm suggesting that the first steps are facilitated by friendly neutrals).
The referendum of May 1870 was indeed carefully worded, but it was associating the approval of constitutional reforms with the future of the dynasty.
The use of plebiscite itself, even if it was a fundamental principle of bonapartism, was very reduced, only used three times (1851 to approve the coup of 2 December, in 1852 to restore the Empire, in 1870 for the constitutional reform). This is explained by the will of Napoléon III not to depreciate the value of the plebiscite by repeated use, and the abusive use you mention isn't likely to happen for the same reason (along with the consequent risk of failure). In the way of probing opinion, he used the legislative elections which despite the system of official candidates, didn't prevent independent and opposition candidates from running, and as such, the elections of 1863 and 1869 were instrumental, particularly the latter one.
Even in 1870, Napoléon III reluctantly used the plebiscite (maybe fearing another setback after the previous elections) but that position was defended by a number of officials, including Rouher and Prince Napoleon who judged it necessary to anchor its popular legitimacy.
The plebiscites of 1851 and 1852 happened in a completely different context and IMHO were justified by the momentous change to the form of government. The plebiscite of 1870 is a horse of quite a different color and could become a dangerous precedent. While I admit that between 1852 and 1870 Louis Napoleon refrained from using plebiscites, I would say that he never had a real need for them before the crisis of 1869-70.
I do agree, in 1870 the Prince is still a white page. However even if the emperor does not abdicate (quite possible without Sedan and with a quick peace) his health is deteriorating fast. I can accept that he has still the energy to achieve a peace treaty, but after it I doubt he may have the strength for a hands-on government style: this means that the empress will be a kind of unofficial regent (and an official one after his death) and will have a lot of influence on the education of the Prince, in particular shielding him from those she considers dangerous influences.As for the Prince Imperial's political position, I would not presume as IOTL, what we know of it was conditionned by the trauma of exile. Without exile, the Prince would be much less under Eugénie's influence and more courted by politicians, other members of the imperial court...
As for the diplomatic position of France, the good relations with Great Britain may not survive Napoléon III who was the main proponent of them. Unless Napoléon IV shows the same anglophilia and the same will in defending it, the colonial race may well create an important rift between London and Paris.
If the war still happens, Rome garrison would still be evacuated (a prerequisite to support from Italy) as it was IOTL, solving the Roman question as a fait accompli. There might still be tensions over it, but I think that the colonial race would be more sensitive. Relations may depend on how much Paris is willing to make a compromise with Italians, especially over Tunisia where the Italian interests were important and of which the occupation in 1881 IOTL by France had thrown Italy into Berlin's arms.
Also, with the imperial regime still existing, France would be less of a pariah and there may be chances of Franz-Joseph more willing to ally with it than he was with the Third Republic.
A rational, stable France should not have any doubt in pursuing an Anglophile policy (it did not happen IOTL until after Fashoda, but the Third Republic was not exactly a stable regime).
I am not really sure what might be the benefit for France in entering an alliance with Austria (and viceversa, btw), unless it is purely an anti-German defensive pact: it might make more sense if the Southern German states remain independent.
The relations with Italy are a bit more complex: IOTL after Sedan the Roman question was already answered (Austria had also promised not to intervene). ITTL it might be trickier, given the persisting opposition of the French catholics. There is also the problem of the commercial war which between France and Italy during the 1870s (agricultural exports mainly, but also Italian migrants in France). This came before the "slap of Tunis", and will be more difficult to deal with rationally. IIRC, IOTL Gambetta tried to mend the fences with Italy toward the end of the 1870s but it was probably too late and the occupation of Tunis in 1881 sealed the enmity.
I did not say that Ollivier was "adamant" about going to war. My point is that he was afraid to be criticized if he opposed it, same as Rouher was criticized in 1866 for the failure to intervene on Austria's behalf. Hence both his passivity and his acceptance of the war ''with a light heart''.As for Ollivier, I wouldn't say he was so adamant about going to war. He was here passive, but if Napoléon III was passive by sickness, Ollivier was by choice (maybe he thought there was no risk accepting the war, saying he accepted the war ''with a light heart'').