What about this:
[KVS Availability Tool 2.1.0/Platinum - Apollo: ITN/CWT/US-CA]
Code:
FRA Frankfurt Metro / Frankfurt Int'l DE = FRA HHN [EDDF]
SYD Sydney Kingsford Smith NS AU [YSSY]
FRI 14 Jul 2006
Carrier Flight From Depart To Arrive A/C St Availability
--------- ------ ---- --------- ---- --------- ---- -- --------------------------------------
LH 782 FRA 22:35 BKK 13:55 +1 747 0 F9 A9 C9 D9 Z0 Y9 B9 M9 H9 Q9 V1 W0 S0
-> LH/TG 9744 BKK 18:15 +1 SYD 06:15 +2 747 0 F0 A4 C4 D0 Z0 Y0 B4 M0 H4 Q0 V0 W0 S0
You'll arrive at 6:15am on the 16th. Time to grab a cab to the CBD, but probably no shower.

The availability looks fishy on the LH/TG codeshare, but it seems to be there. You'll have to get CDG-FRA, but that shouldn't be too hard, there are lots of availability on good connections:
[KVS Availability Tool 2.1.0/Platinum - Apollo: ITN/CWT/US-CA]
Code:
CDG Paris Ch De Gaulle FR [LFPG]
FRA Frankfurt Metro / Frankfurt Int'l DE = FRA HHN [EDDF]
FRI 14 Jul 2006
Carrier Flight From Depart To Arrive A/C St Availability
--------- ------ ---- --------- ---- --------- ---- -- --------------------------------------------------
LH 4227 CDG 18:45 FRA 20:05 32S 0 C9 D4 Z0 Y9 B9 M9 H9 Q9 V9 W9 U0 S0 G0 K0 L0 T0 E0
LH 4229 CDG 19:40 FRA 21:00 737 0 C9 D9 Z9 Y9 B9 M9 H9 Q9 V9 W9 U0 S9 G9 K0 L0 T0 E0
LH 4231 CDG 20:25 FRA 21:45 737 0 C9 D9 Z9 Y9 B9 M9 H9 Q9 V9 W9 U0 S9 G0 K0 L0 T0 E0
LH 4233 CDG 21:30 FRA 22:40 737 0 C9 D9 Z9 Y9 B9 M9 H9 Q9 V9 W9 U9 S9 G9 K9 L9 T9 E9