The Working Families Party has endorsed Councilman Bill de Blasio, in his run for public advocate. De Blasio is a Democrat, and most of the WFP’s members are registered with the party. Here’s an excerpt:
BROOKLYN – The Working Families Party recently entered the fray of New York City electoral politics once again when it endorsed Brooklyn’s Councilman Bill de Blasio (D-Carroll Gardens/Cobble Hill/Park Slope/Kensington) in de Blasio’s race for public advocate.
De Blasio is running for the Democratic Party nomination for public advocate against Mark Green, the former public advocate who has lost quite a few races since then; former New York Civil Liberties Union Director Norman Siegel; and fellow Councilman Eric Gioia (D-Queens).
You can read the full article here. Source: Brooklyn Daily Eagle.

The WFP should be classified as “Democratic Party”, since almost all of their electoral activity consists of endorsing Democrats.
That is where they belong, yes.
I wasn’t sure if the WFP would be under “Socialist/left parties,” they certainly seem left-wing.