Two major Fallschirmjager units fought in the Ardennes in 1944-45, these were the 3rd and 5th Fallschirmjager Divisions composed of the 5th, 8th, and 9th FsJ Regt's in the former and the 13th, 14th, and 15th FsJ Regt's in the latter. Note that there were many subunits as well as the 11th FsJ Sturmgeschutz Brigade attached to the 5th FsJ Div.
The Fallschirmjager with Peiper were from a battalion of the 9th FsJ Regiment of the 3rd Fsj Div. Peiper pretty much attached them to his command and these were the troops you famously see riding a King Tiger tank through the forest. They were with Peiper, but not necessarily under him the whole time. The 3rd and 5th FsJ Div's fought under their own command for the most part.
There was also von der Heydte's specially formed unit that parachuted into the Ardennes. Most misdropped or were not able to drop and many were captured (including von der Heydte). This was a specially picked unit.
The information you provide is scant, as there were many Fallschirmjager also fighting on the western front and not necessarily in the Ardennes, like the remnants of the 2nd, 6th, and 7th FsJ Div's and various training Fallschirmjager battalions scattered throughout. There were tens of thousands of Fallschirmjager troops on the western front and pinpointing the unit would be difficult.
Is there any additional information you can provide? Such as where he was captured, where his home station may have been, when he was captured, etc.