Galileo-034 would know better than I on this but it depends a lot on how and who wins the war.
1) Nappie won decisively the war.
That's probably going to be the hardest : french army was barely prepared, badly organised and badly lead. It wasn't doomed to fail, and a better planned war would have gone very differently, especially with the good equipment it had, but it's going to be hard.
You can write off any blunt annexation or dream about left bank of the Rhine. There's no way Britain would accept this.
That said, I could see the annexation of territories lost at the
Treaty of Paris, as Landau, and it could prevent Prussia to fully take on southern German states, preserved as some form of buffer region. Indemnities should be in order.
2) Nappie doesn't loose the war.
The more likely outcome, if Napoleon manages to hold out Prussians, with a long war ongoing is a status-quo ante-bellum for France, and a still ongoing German unification.
Bismarck didn't want a long war, and his goal was more unification than annexation. Once his objective reached on this regard, wasting ressources wouldn't be sound for him.
Both of these would certainly prevent the fall of the IInd Empire under Nappie III, while it's less certain for the future. The problem with charismatic regime is that they depend a lot of circumstances, but for what matter the aftermath of the war, it would be safe.
3) French Republic doesn't loose the war.
It's as hard, but still doable. A bit like 2), the goal is to undergo a war of attrition but there, a long war isn't advised.
Most of elites were opposed to a republican re-establishment, and would take advantage of the situation to destabilize it as a regime of war (as they did IOTL).
If Gambetta offensive was to work properly, effectivly breaking Paris' siege, Bismarck could be tempted to undergo negociations with France still paying reparations.
French army should do really well to prevent territorial losses, but for all the challenge it was at this point, it was still doable playing on Bismarck's political priorities.