[Gud]

Luftwaffe War Establishment (Kriegsstärkenachweisung) 8121(L) dated 1.5.44 gives the following organization for a rifle platoon in a Fallshirmjägerkompanie:

Zugführer (Platoon Leader) Lt,

Zugtrupp (Platoon HQ section)
1 Zugtruppführer (Sec Ldr)
3 Melder (Messenger)
1 Waffenwart (Armorer)

3 Squads, including in total (for all 3 squads)
3 Gruppenführer (Squad Leader)
3 Stellvertretende Gruppenführer (Deputy Squad Leader)
12 Schützen (Riflemen)
12 MG-Schützen (Machinegunners and assistants)
2 Drivers for 3-ton trucks

So about 34-35 soldiers - I'd say 3x11-man squads each with 2xLMG.