Well, actually the "Fuchstanz" ("foxy dance"

) is just a well known spot with two pubs located in the middle of the Taunus.
To answer your question:
Yes - along the mountains located around the Fuchstanz, esp. @ Altkönig, Kleiner & Grosser Feldberg there are several decent singletracks, which will most likely fullfil your needs.
Nevertheless it's quite difficult to describe the location of these trails here. Addtionally some people here do not like, that trails are mentioned or described within the forum, in order to keep them "secret". Actually the Taunus is a very small, but also very popular recreation area and there have been and still are a lot of conflicts between bikers, hikers and forest rangers.
I therefore would suggest to start riding the Taunus, by doing tours with locals.
As already mentioned within this thread, it's very common to start biking at Hohemark, which is also a natural one, for you, arriving from Hanau.
If you are new to the Taunus and want to get an introduction by one of the local biking groups might be of interest for you - I try to mention all of them, just to give you the complete picture:
1.
GoCrazy- This is a travel agency for MTB-travels. As a teaser they offer guided tours to the Taunus at different skill levels. In the summer they start Wednesday, 06:00PM at Hohemark, in the winter I think it's Saturday, 02:00PM. Please note that they charge a fee of 50 Euro per season, which is refunded in case that you book one of their MTB-travels. GoCrazy tours good to get to know the trails in the Taunus, but they are more CC-oriented.
2.
The After Work Bikers (AWBler) - This is a biking community, which has a long history within this forum. They have their own thread. They also start quite frequently on Wednesdays at 06:00 PM at Hohemark to ride the Taunus. Also nice to get to know the Taunus, because you will ride with experienced locals, but also more the CC-type of thing.
3. One other group is the
"Freireiter" (obviously the German translation of "Freerider). They have there own thread too, but currently do not ride that frequently the Taunus (@Freireiters: No offense intended

). These guys also go out to bike parks. The Freireiter also usually start at Hohemark. Quite frequently they use the public bus to shuttle up-hill. If you are looking for almost pure downhill thrill, they might be your choice.
4.
The "Taunus-Plauschers". We also have no regular dates for riding the Taunus and tend to start on the "other end of the Taunus", which is in the area of Kelkheim. Tours usually comprise a sound mixture of both going up and down the hill by bike on Taunus trails. Once or twice per week after work I myself take my bike directly from Frankfurt to Hohemark to ride the Taunus.
5.
Beinhart Bike-Treff on Tuesday and Thursday - They also start in the area of Kelkheim or Hofheim. Very CC-style, but you would get to know a lot of trails, because the guides know the Taunus very well.
Hope that helps!