He didn't really. His regime uses a fair amount of reformist and populist rhetoric, and he was pretty important for some aspects of general economic development (like railway building and urban redevelopment). However, French welfare systems are pretty minimal, ad-hoc and reliant on either local government or private and religious organizations throughout the nineteenth century. The main thing Napoleon III does is issue some legislative reforms which give a bit more freedom and some state recognition to these charitable and mutual aid associations.
Some state welfare provision is put in place during the Third Republic from the 1890s onwards (and picks up in the interwar period), partly in emulation of the German system and partly due to its governing ideologies around the promotion of health and "progress", but it's still relatively small. The big welfare system that we associate with modern France is mainly a product of the post-Second World War era.