Vote to crown Chambord (or ITTL Phillippe) king, sell it as a democratic restoration and repress not only the Paris Commune as IOTL but also anyone else willing to fight them...
And then die, painfully, if they're not able to escape the country once the nation goes up in flames. Your plan is a recipe for a very short lived reactionary uprising, followed by a sharp turn to the left. Expect the radical republicans to dominate the (restored)
IIIe République. Its simply too late at this point for the monarchists to simply install a king without any input at all from the people. However...
Ha, what about a plebiscite for a constitutional monarchy, for the hell of it? Stir up a lil national pride.
This is, IMHO, the most viable route, though I won't rate the chances of success more than perhaps 50/50 - and that's only if it happens immediately after the Franco-Prussian War, no latter than 1873 surely. The problem for the monarchists was that they refused to given in to populism; a parliamentary monarchy along the lines of pre-1832 Reform Britain was as far as they were willing to go. So you need to change that, and it needs to happen immediately after the war, and it needs to be someone who can stir up the crowds into a patriotic fervor. Which means someone other than either Henri or Phillipe.
Perhaps Prince Robert, Duke of Chartres? Unlike his brother he stayed on the continent, and even fought on the French side (as a dragoon officer for the Piedmontese) during the
Campagne d'Italie, and even fought in the Franco-Prussian War by disguising his face and using a pseudonym and fake accent. Hell, even after revealing himself after the war the Third Republic kept him enrolled in the army, and deployed him to Algeria to put down a minor rebellion there. IOTL he stayed in the army until 1881 when the republican government removed him.
Or Henri d'Orleans, who also volunteered to serve in the Franco-Prussian War, and also after being refused tried once more under a disguise, then becoming a divisional general. After the war he resided over the court-martial which condemned Marshal Bazaine to death. He later became Inspector General of the Army, and worked closely with Boulanger during the latter's military reforms. IOTL he nearly launched a coup in response to the 1886 Law of Exile, writing to Jules Grevy that "it is my duty to remind you that the military ranks are above your ability," just days before he was arrested and deported to Belgium. Henri was almost the Orléanist candidate in the place of Phillipe, but the Legitimists considered him 'too liberal.'
Once again though, I must stress that this must happen immediately after the war for it to succeed, and if it does the monarchists are going to be walking a very thin line between harnessing populist patriotic feelings and stirring up revolutionary anti-German revanche.
