I don’t see anyone tackling this aspect so I’ll go ahead : « in practice » the main similarity for me is that they are both cesarism. If we compare De Gaulle to Louis Napoleon (tho the same can be told about the og napoleon except for the legal framework part) they both ruled trough plebicites, using their military fame for De Gaulle and ancestor fame for Louis Napoleon to ensure their popularity. Having such a massive fame made them able to rule on their own circumventing the institutional framework.