Return of the Bonapartists?

I've just seen the news that in the forthcoming French legislative elections, the great great nephew of Napoleon Bonaparte is standing. (BBC News: Napoleon runs for parliament seat) My knowledge of the convoluted history of French politics isn't good enough to recall what exactly what happened to the Bonapartists but I thought they were considered to have been the predecessors to Gaullism or something. Napoleon is running for Francois Bayrou's new party - is this a natural home? Can any readers who know better explain?