Will Kürlich Kerl
Banned
What happens if Napoleon III doesn't coup the 2nd French Republic and form the 2nd French Empire in 1852?
Well... the thing is that the reason for the coup wasn't just Napoleon III's ambitious nature, though that certainly played a role; a coalition of liberal monarchists and leftist republicans, what few of the latter remained anyhow, had joined together in the Assembly to do everything they could to get Napoleon ejected from power. The constitution of the Second Republic would have prevented Napoleon III from running for a second term anyhow, however he'd spent most of 1850/1851 campaigning throughout France to raise support for an amendment to change that. Most of the French people were in favor of it, remember the man was elected by 74%! However the Assembly rejected it, and then further the liberal-republican coalition forced Bonaparte's appointed PM, d'Hautpoul, out of office, and then without anyone to obstruct them they amended the constitution to instead repeal universal suffrage and re-introduce the tax-based voting of the July Monarchy, which limited the vote to only some 1% of the populace, which is why the IOTL coup was fairly universally hailed throughout France.
So, assuming Napoleon III simply takes it on the chin (debatable), and as I'm sure it'd be against the spirit of the OP to have seize control & remain in power as a populist dictator without recreating the empire, this obviously means someone else is going to take charge. The question really is who; my money would be on Thiers as he'd been the leader of the opposition against Napoleon throughout the two years leading up to the IOTL coup, but I'm sure the liberal-republican coalition would break down rather quickly and the far left would run their own candidates to challenge him.
I wonder if perhaps Napoleon might pull a Putin and have some lackey run for President in his stead while Bonaparte himself gets re-elected to the Assembly to act as President of the Council of Ministers. Napoleon had already burnt some bridges with the Parti de l'Ordre by this point, so they very well might split the rightist vote as they run their own candidate while a Bonapartist candidate runs under Napoleon's blessing.