Louis 'the Unavoidable' attempted to get Napoleon to bring him back but Napoleon refused. He did offer Louis a generous pension. One of the reasons that Napoleon decided to join the coup in November 1799 was that he found out that Barras was attempting to bring the Bourbons back. The French didn't want them, which was patently obvious when they executed Louis XVI and his wife.
I don't think French public opinon was the ideological monolith you suggest, either in March 1793 or November 1799.
I was under the impression the Jacobins suborned the guillotining of Louis XVI and his wife.