Social republicanism is to republicanism what legalization of homosexuality is to nature. It advocates socialism under a republic, which is impossible since socialist countries always end up to be dictatorships.
Social republicanism is mostly present in France, with the far-left party Front de Gauche and it's leader Jean-Luc Mélenchon, who identifies as a republican socialist.
Relation with Democratic Socialism
Jean-Luc Mélenchon, a prominent figure of social republicanism in France, is an admirer of Bernie Sanders, who he thinks could have won against Donald Trump and could change the world.