My timeline deals with the premise of a Longer Lasting Second French Empire. Even though it has not gone to 1870 yet, it has already seen French intervention in the alt-Austro-Prussian War and saw Prussia removed as a significant threat (thus butterflying away the Franco-Prussian War...at least as we know it.)
Now it is true that the Second Empire is not as stable as one would think, especially late in it's life (between the end of the OTL Austro-Prussian War, and the Franco-Prussian War) but given time (and a little bit of luck, or smart thinking early on) you will be able to achieve a stable government that France had sorely sought after since the fall of the Ancien Regime.