Durkheim has been a socialist at heart but in a rather guarded way. Assessing such a statement is rather different from offering evidence or proof as it involves dismantling various self-images - that of Durkheim himself and also, at a distance, those of his commentators.
Durkheim refrained from any open commitment to socialism as he (rightly) thought that it would interfere with his stance as an impartial scientist. American scholars, who are loath to be suspected of leftist sympathies, tend to overplay his conservatism. This is more or less the gist of a paper by Pierre Birnbaum (Dimensions du pouvoir, 1984, p.11). Claiming, as he did, that his socialism is the scientific one put him at odds with marxists, his contemporaries and later, who also tended to stress conservative implications of his views. As Raymond Aron noted "he conceived sociology as the scientific counterpart of socialism" (Aron, 1960 p.31).
There is much circumstantial evidence for his sympathy for socialism: Steven Lukes reports that Durkheim often arrived at his lectures carrying a copy of L'Humanite (Lukes, E.Durkheim, his life and works, 1973). It seems that just about everybody around him was a socialist and Mauss, Guesdes, Jaures were among his good friends. "And when Durkheim gave his course on the history of socialist ideas, Jaurès and the other socialist leader Guesde expressed agreement with his definition of socialism." (Thompson K, Durkheim 1982, p.28)