PC: Second French Empire survives the Franco-Prussian War

As the tin says - would it be possible for the Second Empire to survive a defeat in the Franco-Prussian War?

Note, of course, that I mean the Empire itself; Napoleon III can abdicate or whatever.
 
Perhaps the Prussians/Germans could prop it up after a faster victory? Bismarck wanted to keep Napoleon in power, after all, both to avert a republican neighbor and to end the war...
 
There is just to avoid a defeat of the scale of Sedan.
I already discussed such a scenario: https://www.alternatehistory.com/Discussion/showthread.php?t=195264 .
The possibility is the Army of the Rhine escaping Metz after Mars-la-Tour , leading to a protracted winter campaign around Paris, leading to an attrition war that the Prussians can't afford, contrary to the French. That leads Bismarck to accept a white peace, knowing he has already achieved his goal of unifying Germany through a ''defensive'' war.
 
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