There is not a single chance that the brand-new German empire can manage to enforce a harsher peace on France (which btw was not even in the wish list of good old Otto). I'd rather suggest that there are a couple of alternative scenarios which might be more interesting (and realistic).
The first one is a TL where the events of late August-early September 1870 go exactly according to Bismarck's plan: the last French field army in the north is still decisively beaten at Sedan, but Nappy has not followed the army, deciding (correctly IMHO) to go back to Paris and keep the Bonapartist regime alive. ITTL I would expect that a cease fire is agreed by the 10th of September, and a peace treaty would be negotiated by mid October at latest. The peace treaty would be more lenient than IOTL (no Alsace-Lorraine for example; maybe neutralization of A-L and demolition of the main northern fortresses - Metz, Strasbourg and Belfort). I would assume that Bismarck will do his best to avoid a collapse of the second empire, since his worst nightmare was a republican France. This scenario would butterfly away the Commune (although there might be major riots/insurrections in Paris) but might also end up with an attempted coup by Bazaine. France would remain quite unstable and this might hurt the economic recovery of OTL, even if reparations are lower. Another casualty of the butterflies might be the German empire, at least for the time being. It might end up with a Germany united as a confederation.
The other alternative scenario is where the French refuse to accept the OTL peace treaty. The Bonapartist regime is gone, and the German empire has been proclaimed. The Commune is in full swing, and the Germans occupy all of northern France. However Bismarck's position is less than attractive: the economy is going down the hill what with having more than 1 million men under arms for almost one year; there is no way that a complete occupation of France might work, and there is also a limit to the taxation that might be wrung out from Northern France to pay for the occupation costs; the political situation is becoming unsettled in Germany too, with the conservatives refusing additional taxes to pay for the war and the liberals demanding more say in politics. More ominously the diplomatic situation is becoming more and more unsettled: there is no way that such a major disruption of a key European region might be allowed to go on for a long time. There will be international pressure on the German empire and on the French government too, and almost certainly a conference of powers will be convened in summer or early autumn 1871. In this scenario it is unlikely that Germany will get a better peace treaty: my guess is that A-L will certainly be neutralized (same as it happened with Luxembourg) under a joint guarantee of the powers.
I'd think that either scenario would be beneficial to Franco-German relations in the long run, and might butterfly away (or at least make it more difficult) future major wars along the Rhein.