The set Lmc8 posted is for the Free VS, but the feet are the same as fits the later Free Rotary.
From what I've gathered, Free took over New Home around 1927 and after that, the New Home was just a "name" on Free machines. Free and National merged in 1953, and closed in 1957. Janome took over and started putting the name "New Home" on it's machines.
BTW - National had a different style of attachments - and they made most of the Montgomery Wards machines until National went of out of business.
The set for the rotary has a different style shirr plate and underbaider - one item to note, later Greist sets removed the underbraider and used the modified edge stitcher for top braiding.
One identifing detail of the "Free" made machines is the needle plate with these two holes in it.
The underbaider and shirr plate have two hooks on the bottom, and they clip into the holes - tip the attachment and get the clip started in the top hole, then lower it so the bottom one slides in, then push it into place.
The easiest way to get an idea if a set will fit your machine - look at the style of shirr plate and underbraider. Though always accept that someone may have "mixed and matched" if they had more than one set without realizing they weren't quite the same.